From fa0884dec9f5dc5539dcd0e617f0b53ee939fac4 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 30 Jun 2026 15:07:54 +0200
Subject: [PATCH 1/9] rename tags table to structure_tags

---
 databases/catdat/data/config.yaml            |  2 +-
 databases/catdat/schema/001_structures.sql   |  4 ++--
 databases/catdat/scripts/seed.ts             | 12 ++++++------
 databases/catdat/scripts/utils/seed.types.ts |  2 +-
 src/lib/server/fetchers/structure.ts         |  2 +-
 src/lib/server/fetchers/structures.ts        |  2 +-
 src/lib/server/fetchers/tags.ts              |  6 +++---
 src/routes/categories/[tag]/+page.server.ts  |  4 ++--
 src/routes/functors/[tag]/+page.server.ts    |  4 ++--
 9 files changed, 19 insertions(+), 19 deletions(-)

diff --git a/databases/catdat/data/config.yaml b/databases/catdat/data/config.yaml
index 5967987f7..d06c7d9e8 100644
--- a/databases/catdat/data/config.yaml
+++ b/databases/catdat/data/config.yaml
@@ -1,4 +1,4 @@
-shared_tags:
+structure_tags:
   - algebra
   - algebraic geometry
   - analysis
diff --git a/databases/catdat/schema/001_structures.sql b/databases/catdat/schema/001_structures.sql
index ed89d1bff..9662fa6ee 100644
--- a/databases/catdat/schema/001_structures.sql
+++ b/databases/catdat/schema/001_structures.sql
@@ -42,7 +42,7 @@ CREATE TABLE structure_comments (
 
 CREATE INDEX idx_structure_comments ON structure_comments (structure_id);
 
-CREATE TABLE tags (
+CREATE TABLE structure_tags (
     id INTEGER PRIMARY KEY,
     tag TEXT NOT NULL,
     type TEXT NOT NULL,
@@ -56,7 +56,7 @@ CREATE TABLE structure_tag_assignments (
     tag TEXT NOT NULL,
     PRIMARY KEY (structure_id, type, tag),
     FOREIGN KEY (structure_id, type) REFERENCES structures (id, type) ON DELETE CASCADE,
-    FOREIGN KEY (tag, type) REFERENCES tags (tag, type) ON DELETE CASCADE
+    FOREIGN KEY (tag, type) REFERENCES structure_tags (tag, type) ON DELETE CASCADE
 );
 
 CREATE TABLE structure_maps (
diff --git a/databases/catdat/scripts/seed.ts b/databases/catdat/scripts/seed.ts
index 20aa3f024..934270c47 100644
--- a/databases/catdat/scripts/seed.ts
+++ b/databases/catdat/scripts/seed.ts
@@ -79,7 +79,7 @@ function clear_all_tables() {
 		db.prepare(`DELETE FROM related_structures`).run()
 		db.prepare(`DELETE FROM structure_comments`).run()
 		db.prepare(`DELETE FROM structure_tag_assignments`).run()
-		db.prepare(`DELETE FROM tags`).run()
+		db.prepare(`DELETE FROM structure_tags`).run()
 		db.prepare(`DELETE FROM relations`).run()
 
 		// this deletes categories and functors automatically
@@ -98,8 +98,8 @@ function clear_all_tables() {
  * Seeds the data from the global config file `config.yaml`.
  */
 function seed_config() {
-	const tag_insert = db.prepare<[string, StructureType]>(
-		`INSERT INTO tags (tag, type) VALUES (?, ?)`,
+	const structure_tag_insert = db.prepare<[string, StructureType]>(
+		`INSERT INTO structure_tags (tag, type) VALUES (?, ?)`,
 	)
 
 	const relation_insert = db.prepare(
@@ -116,12 +116,12 @@ function seed_config() {
 
 	function insert_config(config: ConfigYaml) {
 		for (const type of STRUCTURES) {
-			for (const tag of config.shared_tags) {
-				tag_insert.run(tag, type)
+			for (const tag of config.structure_tags) {
+				structure_tag_insert.run(tag, type)
 			}
 
 			for (const tag of config[`${type}_tags`]) {
-				tag_insert.run(tag, type)
+				structure_tag_insert.run(tag, type)
 			}
 		}
 
diff --git a/databases/catdat/scripts/utils/seed.types.ts b/databases/catdat/scripts/utils/seed.types.ts
index 01adf4d30..ae5874a51 100644
--- a/databases/catdat/scripts/utils/seed.types.ts
+++ b/databases/catdat/scripts/utils/seed.types.ts
@@ -1,5 +1,5 @@
 export type ConfigYaml = {
-	shared_tags: string[]
+	structure_tags: string[]
 	category_tags: string[]
 	functor_tags: string[]
 	relations: {
diff --git a/src/lib/server/fetchers/structure.ts b/src/lib/server/fetchers/structure.ts
index 05d564a1d..fbfa1e9b2 100644
--- a/src/lib/server/fetchers/structure.ts
+++ b/src/lib/server/fetchers/structure.ts
@@ -55,7 +55,7 @@ export function fetch_structure(type: StructureType, id: string) {
 		sql`
             SELECT st.tag
             FROM structure_tag_assignments st
-            INNER JOIN tags t ON t.tag = st.tag
+            INNER JOIN structure_tags t ON t.tag = st.tag
             WHERE t.type = ${type} AND st.structure_id = ${id}
             ORDER BY t.id
         `,
diff --git a/src/lib/server/fetchers/structures.ts b/src/lib/server/fetchers/structures.ts
index 2fc4af8c7..cc60c6bc8 100644
--- a/src/lib/server/fetchers/structures.ts
+++ b/src/lib/server/fetchers/structures.ts
@@ -27,7 +27,7 @@ export function fetch_structures_and_tags(type: StructureType) {
             ORDER BY lower(name)`,
 		sql`
             SELECT t.tag
-            FROM tags t
+            FROM structure_tags t
             WHERE t.type = ${type}
             AND EXISTS (
                 SELECT 1 FROM structure_tag_assignments a
diff --git a/src/lib/server/fetchers/tags.ts b/src/lib/server/fetchers/tags.ts
index 6a925b399..02dec9623 100644
--- a/src/lib/server/fetchers/tags.ts
+++ b/src/lib/server/fetchers/tags.ts
@@ -2,12 +2,12 @@ import type { StructureType, TagObject } from '$lib/commons/types'
 import sql from 'sql-template-tag'
 import { query } from '$lib/server/db.catdat'
 
-export function fetch_tags(type: StructureType) {
+export function fetch_structure_tags(type: StructureType) {
 	const { rows, err } = query<TagObject>(sql`
-		SELECT tag FROM tags WHERE type = ${type}
+		SELECT tag FROM structure_tags WHERE type = ${type}
 	`)
 
-	if (err) throw new Error('Database error: Failed to load tags')
+	if (err) throw new Error('Database error: Failed to load structure tags')
 
 	return rows
 }
diff --git a/src/routes/categories/[tag]/+page.server.ts b/src/routes/categories/[tag]/+page.server.ts
index 7c1f5fc06..2dabfdeeb 100644
--- a/src/routes/categories/[tag]/+page.server.ts
+++ b/src/routes/categories/[tag]/+page.server.ts
@@ -1,9 +1,9 @@
 import type { EntryGenerator } from './$types'
 import { fetch_tagged_structures } from '$lib/server/fetchers/structures'
-import { fetch_tags } from '$lib/server/fetchers/tags'
+import { fetch_structure_tags } from '$lib/server/fetchers/tags'
 
 export const entries: EntryGenerator = () => {
-	return fetch_tags('category')
+	return fetch_structure_tags('category')
 }
 
 export const load = (event) => {
diff --git a/src/routes/functors/[tag]/+page.server.ts b/src/routes/functors/[tag]/+page.server.ts
index 7c7b5dec9..b0131707c 100644
--- a/src/routes/functors/[tag]/+page.server.ts
+++ b/src/routes/functors/[tag]/+page.server.ts
@@ -1,9 +1,9 @@
 import type { EntryGenerator } from './$types'
 import { fetch_tagged_structures } from '$lib/server/fetchers/structures'
-import { fetch_tags } from '$lib/server/fetchers/tags'
+import { fetch_structure_tags } from '$lib/server/fetchers/tags'
 
 export const entries: EntryGenerator = () => {
-	return fetch_tags('functor')
+	return fetch_structure_tags('functor')
 }
 
 export const load = (event) => {

From 57f2d74ee3d898ad5f62d7904c58a5e6ef3a805f Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Tue, 30 Jun 2026 15:32:01 +0200
Subject: [PATCH 2/9] move structure detail page file to pages folder

---
 src/{components => pages}/StructureDetailPage.svelte | 0
 src/routes/category/[id]/+page.svelte                | 2 +-
 src/routes/functor/[id]/+page.svelte                 | 2 +-
 3 files changed, 2 insertions(+), 2 deletions(-)
 rename src/{components => pages}/StructureDetailPage.svelte (100%)

diff --git a/src/components/StructureDetailPage.svelte b/src/pages/StructureDetailPage.svelte
similarity index 100%
rename from src/components/StructureDetailPage.svelte
rename to src/pages/StructureDetailPage.svelte
diff --git a/src/routes/category/[id]/+page.svelte b/src/routes/category/[id]/+page.svelte
index 19de4676c..daeb50bb9 100644
--- a/src/routes/category/[id]/+page.svelte
+++ b/src/routes/category/[id]/+page.svelte
@@ -2,7 +2,7 @@
 	import TextWithProof from '$components/TextWithProof.svelte'
 	import { faQuestion } from '@fortawesome/free-solid-svg-icons'
 	import Fa from 'svelte-fa'
-	import StructureDetailPage from '$components/StructureDetailPage.svelte'
+	import StructureDetailPage from '$pages/StructureDetailPage.svelte'
 
 	let { data } = $props()
 </script>
diff --git a/src/routes/functor/[id]/+page.svelte b/src/routes/functor/[id]/+page.svelte
index 6d75a4300..7d708bb00 100644
--- a/src/routes/functor/[id]/+page.svelte
+++ b/src/routes/functor/[id]/+page.svelte
@@ -1,5 +1,5 @@
 <script lang="ts">
-	import StructureDetailPage from '$components/StructureDetailPage.svelte'
+	import StructureDetailPage from '$pages/StructureDetailPage.svelte'
 
 	let { data } = $props()
 </script>

From d65671ed8e01624b9f21423116852ebcd6a77113 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 09:00:14 +0200
Subject: [PATCH 3/9] add support for property tags

---
 databases/catdat/data/config.yaml             |  4 ++
 databases/catdat/schema/002_properties.sql    | 19 +++++++-
 databases/catdat/scripts/seed.ts              | 21 ++++++++
 databases/catdat/scripts/utils/seed.types.ts  |  3 ++
 src/components/TagList.svelte                 |  9 +++-
 src/lib/server/fetchers/properties.ts         | 48 ++++++++++++++++---
 src/lib/server/fetchers/property.ts           | 15 ++++++
 src/lib/server/fetchers/tags.ts               | 10 ++++
 src/pages/PropertyListPage.svelte             | 18 ++++++-
 src/pages/PropertyPage.svelte                 |  8 ++++
 src/pages/StructureDetailPage.svelte          |  2 +-
 src/pages/StructureListPage.svelte            |  2 +-
 src/pages/TaggedPropertiesPage.svelte         | 27 +++++++++++
 ...age.svelte => TaggedStructuresPage.svelte} |  0
 src/routes/categories/[tag]/+page.svelte      |  4 +-
 .../category-properties/+page.server.ts       |  4 +-
 .../category-properties/[tag]/+page.server.ts | 11 +++++
 .../category-properties/[tag]/+page.svelte    |  7 +++
 src/routes/functor-properties/+page.server.ts |  4 +-
 .../functor-properties/[tag]/+page.server.ts  | 11 +++++
 .../functor-properties/[tag]/+page.svelte     |  7 +++
 src/routes/functors/[tag]/+page.svelte        |  4 +-
 22 files changed, 218 insertions(+), 20 deletions(-)
 create mode 100644 src/pages/TaggedPropertiesPage.svelte
 rename src/pages/{TaggedPage.svelte => TaggedStructuresPage.svelte} (100%)
 create mode 100644 src/routes/category-properties/[tag]/+page.server.ts
 create mode 100644 src/routes/category-properties/[tag]/+page.svelte
 create mode 100644 src/routes/functor-properties/[tag]/+page.server.ts
 create mode 100644 src/routes/functor-properties/[tag]/+page.svelte

diff --git a/databases/catdat/data/config.yaml b/databases/catdat/data/config.yaml
index d06c7d9e8..cf810c3a0 100644
--- a/databases/catdat/data/config.yaml
+++ b/databases/catdat/data/config.yaml
@@ -18,6 +18,10 @@ functor_tags:
   - forgetful
   - free
 
+category_property_tags: []
+
+functor_property_tags: []
+
 relations:
   - relation: is
     conditional: would be
diff --git a/databases/catdat/schema/002_properties.sql b/databases/catdat/schema/002_properties.sql
index 72b995f84..64e830183 100644
--- a/databases/catdat/schema/002_properties.sql
+++ b/databases/catdat/schema/002_properties.sql
@@ -52,4 +52,21 @@ CREATE TABLE property_assignments (
         REFERENCES properties (id, type) ON DELETE CASCADE
 );
 
-CREATE INDEX idx_property_assigned ON property_assignments (property_id);
\ No newline at end of file
+CREATE INDEX idx_property_assigned ON property_assignments (property_id);
+
+CREATE TABLE property_tags (
+    id INTEGER PRIMARY KEY,
+    tag TEXT NOT NULL,
+    type TEXT NOT NULL,
+    UNIQUE (tag, type),
+    FOREIGN KEY (type) REFERENCES structure_types (type) ON DELETE RESTRICT
+);
+
+CREATE TABLE property_tag_assignments (
+    property_id TEXT NOT NULL,
+    type TEXT NOT NULL,
+    tag TEXT NOT NULL,
+    PRIMARY KEY (property_id, type, tag),
+    FOREIGN KEY (property_id, type) REFERENCES properties (id, type) ON DELETE CASCADE,
+    FOREIGN KEY (tag, type) REFERENCES property_tags (tag, type) ON DELETE CASCADE
+);
\ No newline at end of file
diff --git a/databases/catdat/scripts/seed.ts b/databases/catdat/scripts/seed.ts
index 934270c47..ffe8ca2be 100644
--- a/databases/catdat/scripts/seed.ts
+++ b/databases/catdat/scripts/seed.ts
@@ -74,6 +74,8 @@ function clear_all_tables() {
 
 		db.prepare(`DELETE FROM property_assignments`).run()
 		db.prepare(`DELETE FROM related_properties`).run()
+		db.prepare(`DELETE FROM property_tag_assignments`).run()
+		db.prepare(`DELETE FROM property_tags`).run()
 		db.prepare(`DELETE FROM properties`).run()
 
 		db.prepare(`DELETE FROM related_structures`).run()
@@ -102,6 +104,10 @@ function seed_config() {
 		`INSERT INTO structure_tags (tag, type) VALUES (?, ?)`,
 	)
 
+	const property_tag_insert = db.prepare<[string, StructureType]>(
+		`INSERT INTO property_tags (tag, type) VALUES (?, ?)`,
+	)
+
 	const relation_insert = db.prepare(
 		`INSERT INTO relations (relation, conditional) VALUES (?, ?)`,
 	)
@@ -123,6 +129,10 @@ function seed_config() {
 			for (const tag of config[`${type}_tags`]) {
 				structure_tag_insert.run(tag, type)
 			}
+
+			for (const tag of config[`${type}_property_tags`]) {
+				property_tag_insert.run(tag, type)
+			}
 		}
 
 		for (const { relation, conditional } of config.relations) {
@@ -303,6 +313,12 @@ function seed_properties({ type, folder }: { type: StructureType; folder: string
 		VALUES (?, ?, ?)`,
 	)
 
+	const tag_insert = db.prepare(
+		`INSERT INTO property_tag_assignments
+			(property_id, tag, type)
+		VALUES (?, ?, ?)`,
+	)
+
 	function insert_property(property: PropertyYaml) {
 		property_insert.run(
 			property.id,
@@ -317,6 +333,11 @@ function seed_properties({ type, folder }: { type: StructureType; folder: string
 		for (const related of property.related_properties) {
 			related_insert.run(property.id, related, type)
 		}
+
+		for (const tag of property.tags ?? []) {
+			// TODO: remove ?? when tags are filled
+			tag_insert.run(property.id, tag, type)
+		}
 	}
 
 	seed_files(
diff --git a/databases/catdat/scripts/utils/seed.types.ts b/databases/catdat/scripts/utils/seed.types.ts
index ae5874a51..932569e15 100644
--- a/databases/catdat/scripts/utils/seed.types.ts
+++ b/databases/catdat/scripts/utils/seed.types.ts
@@ -2,6 +2,8 @@ export type ConfigYaml = {
 	structure_tags: string[]
 	category_tags: string[]
 	functor_tags: string[]
+	category_property_tags: string[]
+	functor_property_tags: string[]
 	relations: {
 		relation: string
 		conditional: string
@@ -71,6 +73,7 @@ export type PropertyYaml = {
 	dual_property?: string | null
 	invariant_under_equivalences: boolean
 	related_properties: string[]
+	tags?: string[]
 }
 
 export type ImplicationYaml = {
diff --git a/src/components/TagList.svelte b/src/components/TagList.svelte
index 0f7a986ae..6323ae2b5 100644
--- a/src/components/TagList.svelte
+++ b/src/components/TagList.svelte
@@ -8,12 +8,17 @@
 	type Props = {
 		type: StructureType
 		tags: string[]
+		sort: 'structure' | 'property'
 	}
 
-	let { type, tags }: Props = $props()
+	let { type, tags, sort }: Props = $props()
 
 	function filter_by_tag(tag: string) {
-		goto(`/${PLURALS[type]}/${tag}`)
+		if (sort === 'structure') {
+			goto(`/${PLURALS[type]}/${tag}`)
+		} else {
+			goto(`/${type}-properties/${tag}`)
+		}
 	}
 </script>
 
diff --git a/src/lib/server/fetchers/properties.ts b/src/lib/server/fetchers/properties.ts
index 89d270fce..8dbd4ca8d 100644
--- a/src/lib/server/fetchers/properties.ts
+++ b/src/lib/server/fetchers/properties.ts
@@ -1,6 +1,11 @@
-import type { GroupedPropertyShort, StructureType } from '$lib/commons/types'
+import type {
+	GroupedPropertyShort,
+	PropertyShort,
+	StructureType,
+	TagObject,
+} from '$lib/commons/types'
 import sql from 'sql-template-tag'
-import { query } from '$lib/server/db.catdat'
+import { query, batch } from '$lib/server/db.catdat'
 import { error } from '@sveltejs/kit'
 
 export function get_property_ids(type: StructureType) {
@@ -17,16 +22,32 @@ export function get_property_ids(type: StructureType) {
 	return rows.map(({ id }) => id)
 }
 
-export function get_grouped_properties(type: StructureType) {
-	const { rows: properties, err } = query<GroupedPropertyShort>(sql`
+export function fetch_grouped_properties_and_tags(type: StructureType) {
+	const { results, err } = batch<[GroupedPropertyShort, TagObject]>([
+		sql`
 		SELECT id, relation, dual_property_id
 		FROM properties
 		WHERE type = ${type}
 		ORDER BY lower(id)
-	`)
+	`,
+		sql`
+			SELECT t.tag
+			FROM property_tags t
+			WHERE t.type = ${type}
+			AND EXISTS (
+				SELECT 1 FROM property_tag_assignments a
+				WHERE a.tag = t.tag AND a.type = ${type}
+			)
+			ORDER BY t.id
+		`,
+	])
 
 	if (err) error(500, 'Failed to load properties')
 
+	const [properties, tag_objects] = results
+
+	const tags = tag_objects.map(({ tag }) => tag)
+
 	const seen = new Set()
 
 	const grouped_properties: typeof properties = []
@@ -54,5 +75,20 @@ export function get_grouped_properties(type: StructureType) {
 	const total = properties.length
 	const grouped_total = grouped_properties.length
 
-	return { grouped_properties, total, grouped_total }
+	return { grouped_properties, total, grouped_total, tags }
+}
+
+export function fetch_tagged_properties(type: StructureType, tag: string) {
+	const { rows: properties, err } = query<PropertyShort>(sql`
+		SELECT p.id, p.relation
+		FROM property_tag_assignments t
+		INNER JOIN properties p
+		ON p.id = t.property_id
+		WHERE t.tag = ${tag} AND t.type = ${type}
+		ORDER BY lower(id)
+	`)
+
+	if (err) error(500, `Properties could not be loaded`)
+
+	return { properties, tag }
 }
diff --git a/src/lib/server/fetchers/property.ts b/src/lib/server/fetchers/property.ts
index 39ab64bc3..5677f693c 100644
--- a/src/lib/server/fetchers/property.ts
+++ b/src/lib/server/fetchers/property.ts
@@ -3,6 +3,7 @@ import type {
 	StructureShort,
 	PropertyDB,
 	StructureType,
+	TagObject,
 } from '$lib/commons/types'
 import { batch } from '$lib/server/db.catdat'
 import { display_implication, display_property } from '$lib/server/transforms'
@@ -14,6 +15,7 @@ export function fetch_property(type: StructureType, id: string) {
 		[
 			PropertyDB,
 			{ id: string },
+			TagObject,
 			ImplicationDB,
 			StructureShort & { is_satisfied: 0 | 1 | null },
 			StructureShort,
@@ -37,6 +39,15 @@ export function fetch_property(type: StructureType, id: string) {
             FROM related_properties
             WHERE property_id = ${id}
             ORDER BY lower(id)
+        `,
+		// tags
+		sql`
+            SELECT pt.tag
+            FROM property_tag_assignments pt
+            INNER JOIN property_tags t
+                ON t.tag = pt.tag AND t.type = ${type}
+            WHERE pt.property_id = ${id} AND pt.type = ${type}
+            ORDER BY t.id
         `,
 		// relevant implications
 		sql`
@@ -95,6 +106,7 @@ export function fetch_property(type: StructureType, id: string) {
 	const [
 		properties,
 		related,
+		tag_objects,
 		relevant_implications_db,
 		known_structures,
 		unknown_structures,
@@ -108,6 +120,8 @@ export function fetch_property(type: StructureType, id: string) {
 
 	const related_properties = related.map(({ id }) => id)
 
+	const tags = tag_objects.map(({ tag }) => tag)
+
 	const examples = known_structures.filter((f) => f.is_satisfied === 1)
 	const counterexamples = known_structures.filter((f) => f.is_satisfied === 0)
 	const undecidable_structures = known_structures.filter((f) => f.is_satisfied === null)
@@ -123,6 +137,7 @@ export function fetch_property(type: StructureType, id: string) {
 	return {
 		property,
 		related_properties,
+		tags,
 		examples,
 		counterexamples,
 		unknown_structures,
diff --git a/src/lib/server/fetchers/tags.ts b/src/lib/server/fetchers/tags.ts
index 02dec9623..99d118b73 100644
--- a/src/lib/server/fetchers/tags.ts
+++ b/src/lib/server/fetchers/tags.ts
@@ -11,3 +11,13 @@ export function fetch_structure_tags(type: StructureType) {
 
 	return rows
 }
+
+export function fetch_property_tags(type: StructureType) {
+	const { rows, err } = query<TagObject>(sql`
+		SELECT tag FROM property_tags WHERE type = ${type}
+	`)
+
+	if (err) throw new Error('Database error: Failed to load property tags')
+
+	return rows
+}
diff --git a/src/pages/PropertyListPage.svelte b/src/pages/PropertyListPage.svelte
index 29b391902..f556458af 100644
--- a/src/pages/PropertyListPage.svelte
+++ b/src/pages/PropertyListPage.svelte
@@ -2,6 +2,7 @@
 	import MetaData from '$components/MetaData.svelte'
 	import SearchFilter from '$components/SearchFilter.svelte'
 	import SuggestionForm from '$components/SuggestionForm.svelte'
+	import TagList from '$components/TagList.svelte'
 	import { normalize_text, pluralize } from '$lib/client/utils'
 	import { get_property_url } from '$lib/commons/property.url'
 	import { PLURALS } from '$lib/commons/structures'
@@ -14,9 +15,10 @@
 		grouped_properties: GroupedPropertyShort[]
 		total: number
 		grouped_total: number
+		tags: string[]
 	}
 
-	let { type, grouped_properties, total, grouped_total }: Props = $props()
+	let { type, grouped_properties, total, grouped_total, tags }: Props = $props()
 
 	let searched_properties = $derived(
 		search
@@ -63,4 +65,18 @@
 	{/each}
 </ul>
 
+{#if tags.length > 0}
+	<section class="tag-section">
+		<h2>List of tags</h2>
+
+		<TagList {tags} {type} sort="property" />
+	</section>
+{/if}
+
 <SuggestionForm />
+
+<style>
+	.tag-section {
+		margin-top: 2rem;
+	}
+</style>
diff --git a/src/pages/PropertyPage.svelte b/src/pages/PropertyPage.svelte
index 91b8a2d39..8dc08df34 100644
--- a/src/pages/PropertyPage.svelte
+++ b/src/pages/PropertyPage.svelte
@@ -15,11 +15,13 @@
 		StructureType,
 	} from '$lib/commons/types'
 	import { PLURALS } from '$lib/commons/structures'
+	import TagList from '$components/TagList.svelte'
 
 	type Props = {
 		type: StructureType
 		property: PropertyDisplay
 		related_properties: string[]
+		tags: string[]
 		examples: StructureShort[]
 		counterexamples: StructureShort[]
 		unknown_structures: StructureShort[]
@@ -31,6 +33,7 @@
 		type,
 		property,
 		related_properties,
+		tags,
 		examples,
 		counterexamples,
 		unknown_structures,
@@ -43,6 +46,11 @@
 
 <h2>{property.id}</h2>
 
+{#if tags.length}
+	<!-- TODO: remove this if-check later -->
+	<TagList {tags} {type} sort="property" />
+{/if}
+
 <p>
 	{@html property.description}
 
diff --git a/src/pages/StructureDetailPage.svelte b/src/pages/StructureDetailPage.svelte
index c555f7236..0baaa5c7b 100644
--- a/src/pages/StructureDetailPage.svelte
+++ b/src/pages/StructureDetailPage.svelte
@@ -52,7 +52,7 @@
 
 <h2>{structure.name}</h2>
 
-<TagList {tags} {type} />
+<TagList {tags} {type} sort="structure" />
 
 <section aria-label="main info" class="main-info">
 	<ul class="with-margins">
diff --git a/src/pages/StructureListPage.svelte b/src/pages/StructureListPage.svelte
index 622b9c5e6..cb0759f20 100644
--- a/src/pages/StructureListPage.svelte
+++ b/src/pages/StructureListPage.svelte
@@ -58,7 +58,7 @@
 <section>
 	<h2>List of tags</h2>
 
-	<TagList {tags} {type} />
+	<TagList {tags} {type} sort="structure" />
 </section>
 
 <SuggestionForm />
diff --git a/src/pages/TaggedPropertiesPage.svelte b/src/pages/TaggedPropertiesPage.svelte
new file mode 100644
index 000000000..be348d809
--- /dev/null
+++ b/src/pages/TaggedPropertiesPage.svelte
@@ -0,0 +1,27 @@
+<script lang="ts">
+	import MetaData from '$components/MetaData.svelte'
+	import { pluralize } from '$lib/client/utils'
+	import type { PropertyShort, StructureType } from '$lib/commons/types'
+	import PropertyList from '$components/PropertyList.svelte'
+
+	type Props = {
+		type: StructureType
+		properties: PropertyShort[]
+		tag: string
+	}
+
+	let { type, properties, tag }: Props = $props()
+</script>
+
+<MetaData title="List of {type} properties tagged with '{tag}'" />
+
+<h2>List of {type} properties tagged with '{tag}'</h2>
+
+<p class="hint">
+	{pluralize(properties.length, {
+		one: `Found {count} property`,
+		other: `Found {count} properties`,
+	})}
+</p>
+
+<PropertyList {properties} {type} />
diff --git a/src/pages/TaggedPage.svelte b/src/pages/TaggedStructuresPage.svelte
similarity index 100%
rename from src/pages/TaggedPage.svelte
rename to src/pages/TaggedStructuresPage.svelte
diff --git a/src/routes/categories/[tag]/+page.svelte b/src/routes/categories/[tag]/+page.svelte
index e1fa0be6f..23a04e044 100644
--- a/src/routes/categories/[tag]/+page.svelte
+++ b/src/routes/categories/[tag]/+page.svelte
@@ -1,7 +1,7 @@
 <script lang="ts">
-	import TaggedPage from '$pages/TaggedPage.svelte'
+	import TaggedStructuresPage from '$pages/TaggedStructuresPage.svelte'
 
 	let { data } = $props()
 </script>
 
-<TaggedPage type="category" {...data} />
+<TaggedStructuresPage type="category" {...data} />
diff --git a/src/routes/category-properties/+page.server.ts b/src/routes/category-properties/+page.server.ts
index 39f9c2a92..da7dc35a3 100644
--- a/src/routes/category-properties/+page.server.ts
+++ b/src/routes/category-properties/+page.server.ts
@@ -1,5 +1,5 @@
-import { get_grouped_properties } from '$lib/server/fetchers/properties'
+import { fetch_grouped_properties_and_tags } from '$lib/server/fetchers/properties'
 
 export const load = () => {
-	return get_grouped_properties('category')
+	return fetch_grouped_properties_and_tags('category')
 }
diff --git a/src/routes/category-properties/[tag]/+page.server.ts b/src/routes/category-properties/[tag]/+page.server.ts
new file mode 100644
index 000000000..3c7531a70
--- /dev/null
+++ b/src/routes/category-properties/[tag]/+page.server.ts
@@ -0,0 +1,11 @@
+import { fetch_tagged_properties } from '$lib/server/fetchers/properties'
+import { fetch_property_tags } from '$lib/server/fetchers/tags'
+import type { EntryGenerator } from './$types'
+
+export const entries: EntryGenerator = () => {
+	return fetch_property_tags('category')
+}
+
+export const load = (event) => {
+	return fetch_tagged_properties('category', event.params.tag)
+}
diff --git a/src/routes/category-properties/[tag]/+page.svelte b/src/routes/category-properties/[tag]/+page.svelte
new file mode 100644
index 000000000..dbd54b293
--- /dev/null
+++ b/src/routes/category-properties/[tag]/+page.svelte
@@ -0,0 +1,7 @@
+<script lang="ts">
+	import TaggedPropertiesPage from '$pages/TaggedPropertiesPage.svelte'
+
+	let { data } = $props()
+</script>
+
+<TaggedPropertiesPage type="category" {...data} />
diff --git a/src/routes/functor-properties/+page.server.ts b/src/routes/functor-properties/+page.server.ts
index 6635d2729..2e0797ff6 100644
--- a/src/routes/functor-properties/+page.server.ts
+++ b/src/routes/functor-properties/+page.server.ts
@@ -1,5 +1,5 @@
-import { get_grouped_properties } from '$lib/server/fetchers/properties'
+import { fetch_grouped_properties_and_tags } from '$lib/server/fetchers/properties'
 
 export const load = () => {
-	return get_grouped_properties('functor')
+	return fetch_grouped_properties_and_tags('functor')
 }
diff --git a/src/routes/functor-properties/[tag]/+page.server.ts b/src/routes/functor-properties/[tag]/+page.server.ts
new file mode 100644
index 000000000..7c4f183c7
--- /dev/null
+++ b/src/routes/functor-properties/[tag]/+page.server.ts
@@ -0,0 +1,11 @@
+import { fetch_tagged_properties } from '$lib/server/fetchers/properties'
+import { fetch_property_tags } from '$lib/server/fetchers/tags'
+import type { EntryGenerator } from './$types'
+
+export const entries: EntryGenerator = () => {
+	return fetch_property_tags('functor')
+}
+
+export const load = (event) => {
+	return fetch_tagged_properties('functor', event.params.tag)
+}
diff --git a/src/routes/functor-properties/[tag]/+page.svelte b/src/routes/functor-properties/[tag]/+page.svelte
new file mode 100644
index 000000000..8804e18da
--- /dev/null
+++ b/src/routes/functor-properties/[tag]/+page.svelte
@@ -0,0 +1,7 @@
+<script lang="ts">
+	import TaggedPropertiesPage from '$pages/TaggedPropertiesPage.svelte'
+
+	let { data } = $props()
+</script>
+
+<TaggedPropertiesPage type="functor" {...data} />
diff --git a/src/routes/functors/[tag]/+page.svelte b/src/routes/functors/[tag]/+page.svelte
index aa765c464..62d2d5fe8 100644
--- a/src/routes/functors/[tag]/+page.svelte
+++ b/src/routes/functors/[tag]/+page.svelte
@@ -1,7 +1,7 @@
 <script lang="ts">
-	import TaggedPage from '$pages/TaggedPage.svelte'
+	import TaggedStructuresPage from '$pages/TaggedStructuresPage.svelte'
 
 	let { data } = $props()
 </script>
 
-<TaggedPage type="functor" {...data} />
+<TaggedStructuresPage type="functor" {...data} />

From f7ca7c9e1b7da306556d9aaeae1581f22741056c Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 09:05:32 +0200
Subject: [PATCH 4/9] add tags to all properties of categories

---
 .cspell.json                                       |  1 +
 .../data/category-properties/Barr-coexact.yaml     |  4 ++++
 .../data/category-properties/Barr-exact.yaml       |  4 ++++
 databases/catdat/data/category-properties/CIP.yaml |  3 +++
 databases/catdat/data/category-properties/CSP.yaml |  3 +++
 .../data/category-properties/Cauchy complete.yaml  |  5 +++++
 .../category-properties/Grothendieck abelian.yaml  |  3 +++
 .../category-properties/Grothendieck topos.yaml    |  3 +++
 .../catdat/data/category-properties/Malcev.yaml    |  3 +++
 .../catdat/data/category-properties/abelian.yaml   |  5 +++++
 .../data/category-properties/accessible.yaml       |  3 +++
 .../catdat/data/category-properties/additive.yaml  |  6 ++++++
 .../category-properties/aleph1-accessible.yaml     |  3 +++
 .../aleph1-cofiltered limits.yaml                  |  3 +++
 .../category-properties/aleph1-cofiltered.yaml     |  3 +++
 .../aleph1-filtered colimits.yaml                  |  3 +++
 .../data/category-properties/aleph1-filtered.yaml  |  3 +++
 .../category-properties/aleph2-small copowers.yaml |  3 +++
 .../aleph2-small coproducts.yaml                   |  3 +++
 .../category-properties/aleph2-small powers.yaml   |  3 +++
 .../category-properties/aleph2-small products.yaml |  3 +++
 .../catdat/data/category-properties/balanced.yaml  |  3 +++
 .../data/category-properties/binary copowers.yaml  |  3 +++
 .../category-properties/binary coproducts.yaml     |  3 +++
 .../data/category-properties/binary powers.yaml    |  3 +++
 .../data/category-properties/binary products.yaml  |  3 +++
 .../data/category-properties/biproducts.yaml       |  5 +++++
 .../data/category-properties/cartesian closed.yaml |  3 +++
 .../cartesian filtered colimits.yaml               |  3 +++
 .../catdat/data/category-properties/co-Malcev.yaml |  3 +++
 .../data/category-properties/coaccessible.yaml     |  3 +++
 .../category-properties/cocartesian coclosed.yaml  |  3 +++
 .../cocartesian cofiltered limits.yaml             |  3 +++
 .../data/category-properties/cocomplete.yaml       |  3 +++
 .../data/category-properties/codistributive.yaml   |  3 +++
 .../data/category-properties/coequalizers.yaml     |  3 +++
 .../data/category-properties/coextensive.yaml      |  3 +++
 .../category-properties/cofiltered limits.yaml     |  3 +++
 .../cofiltered-limit-stable epimorphisms.yaml      |  4 ++++
 .../data/category-properties/cofiltered.yaml       |  3 +++
 .../data/category-properties/cogenerating set.yaml |  3 +++
 .../data/category-properties/cogenerator.yaml      |  4 ++++
 .../catdat/data/category-properties/cokernels.yaml |  3 +++
 .../catdat/data/category-properties/complete.yaml  |  3 +++
 .../category-properties/connected colimits.yaml    |  3 +++
 .../data/category-properties/connected limits.yaml |  3 +++
 .../catdat/data/category-properties/connected.yaml |  3 +++
 .../catdat/data/category-properties/conormal.yaml  |  3 +++
 .../catdat/data/category-properties/copowers.yaml  |  3 +++
 .../data/category-properties/coproducts.yaml       |  3 +++
 .../coquotients of cocongruences.yaml              |  4 ++++
 .../catdat/data/category-properties/core-thin.yaml |  3 +++
 .../coreflexive equalizers.yaml                    |  3 +++
 .../catdat/data/category-properties/coregular.yaml |  3 +++
 .../data/category-properties/cosifted limits.yaml  |  3 +++
 .../catdat/data/category-properties/cosifted.yaml  |  3 +++
 .../catdat/data/category-properties/counital.yaml  |  3 +++
 .../category-properties/countable copowers.yaml    |  3 +++
 .../category-properties/countable coproducts.yaml  |  3 +++
 .../data/category-properties/countable powers.yaml |  3 +++
 .../category-properties/countable products.yaml    |  3 +++
 .../catdat/data/category-properties/countable.yaml |  4 ++++
 .../countably codistributive.yaml                  |  3 +++
 .../countably distributive.yaml                    |  3 +++
 .../catdat/data/category-properties/direct.yaml    |  4 ++++
 .../category-properties/directed colimits.yaml     |  3 +++
 .../data/category-properties/directed limits.yaml  |  3 +++
 .../catdat/data/category-properties/discrete.yaml  |  4 ++++
 .../category-properties/disjoint coproducts.yaml   |  3 +++
 .../disjoint finite coproducts.yaml                |  3 +++
 .../disjoint finite products.yaml                  |  3 +++
 .../category-properties/disjoint products.yaml     |  3 +++
 .../data/category-properties/distributive.yaml     |  3 +++
 .../effective cocongruences.yaml                   |  3 +++
 .../category-properties/effective congruences.yaml |  3 +++
 .../data/category-properties/elementary topos.yaml |  3 +++
 .../data/category-properties/epi-regular.yaml      |  3 +++
 .../data/category-properties/equalizers.yaml       |  3 +++
 .../category-properties/essentially countable.yaml |  3 +++
 .../category-properties/essentially discrete.yaml  |  3 +++
 .../category-properties/essentially finite.yaml    |  3 +++
 .../category-properties/essentially small.yaml     |  3 +++
 .../exact cofiltered limits.yaml                   |  3 +++
 .../exact filtered colimits.yaml                   |  3 +++
 .../catdat/data/category-properties/extensive.yaml |  3 +++
 .../category-properties/filtered colimits.yaml     |  3 +++
 .../filtered-colimit-stable monomorphisms.yaml     |  4 ++++
 .../catdat/data/category-properties/filtered.yaml  |  3 +++
 .../category-properties/finitary algebraic.yaml    |  3 +++
 .../data/category-properties/finite copowers.yaml  |  3 +++
 .../category-properties/finite coproducts.yaml     |  3 +++
 .../data/category-properties/finite powers.yaml    |  3 +++
 .../data/category-properties/finite products.yaml  |  3 +++
 .../catdat/data/category-properties/finite.yaml    |  4 ++++
 .../category-properties/finitely accessible.yaml   |  3 +++
 .../category-properties/finitely cocomplete.yaml   |  3 +++
 .../category-properties/finitely complete.yaml     |  3 +++
 .../catdat/data/category-properties/gaunt.yaml     |  4 ++++
 .../category-properties/generalized variety.yaml   |  3 +++
 .../data/category-properties/generating set.yaml   |  3 +++
 .../catdat/data/category-properties/generator.yaml |  4 ++++
 .../catdat/data/category-properties/groupoid.yaml  |  3 +++
 .../infinitary codistributive.yaml                 |  3 +++
 .../infinitary coextensive.yaml                    |  3 +++
 .../infinitary distributive.yaml                   |  3 +++
 .../category-properties/infinitary extensive.yaml  |  3 +++
 .../catdat/data/category-properties/inhabited.yaml |  3 +++
 .../data/category-properties/initial object.yaml   |  3 +++
 .../catdat/data/category-properties/inverse.yaml   |  4 ++++
 .../catdat/data/category-properties/kernels.yaml   |  3 +++
 .../category-properties/left cancellative.yaml     |  3 +++
 .../locally aleph1-presentable.yaml                |  3 +++
 .../locally cartesian closed.yaml                  |  3 +++
 .../locally cocartesian coclosed.yaml              |  3 +++
 .../category-properties/locally copresentable.yaml |  3 +++
 .../locally essentially small.yaml                 |  3 +++
 .../data/category-properties/locally finite.yaml   |  3 +++
 .../locally finitely multi-presentable.yaml        |  3 +++
 .../locally finitely presentable.yaml              |  3 +++
 .../locally multi-presentable.yaml                 |  3 +++
 .../locally poly-presentable.yaml                  |  3 +++
 .../category-properties/locally presentable.yaml   |  3 +++
 .../data/category-properties/locally small.yaml    |  4 ++++
 .../locally strongly finitely presentable.yaml     |  4 ++++
 .../data/category-properties/mono-regular.yaml     |  3 +++
 .../data/category-properties/multi-algebraic.yaml  |  3 +++
 .../data/category-properties/multi-cocomplete.yaml |  3 +++
 .../data/category-properties/multi-complete.yaml   |  3 +++
 .../category-properties/multi-initial object.yaml  |  3 +++
 .../category-properties/multi-terminal object.yaml |  3 +++
 .../natural numbers object.yaml                    |  3 +++
 .../catdat/data/category-properties/normal.yaml    |  3 +++
 .../catdat/data/category-properties/one-way.yaml   |  3 +++
 .../catdat/data/category-properties/pointed.yaml   |  3 +++
 .../catdat/data/category-properties/powers.yaml    |  3 +++
 .../data/category-properties/preadditive.yaml      |  3 +++
 .../catdat/data/category-properties/pretopos.yaml  |  4 ++++
 .../catdat/data/category-properties/products.yaml  |  3 +++
 .../catdat/data/category-properties/pullbacks.yaml |  3 +++
 .../catdat/data/category-properties/pushouts.yaml  |  3 +++
 .../quotient object classifier.yaml                |  3 +++
 .../data/category-properties/quotient-trivial.yaml |  3 +++
 .../quotients of congruences.yaml                  |  4 ++++
 .../reflexive coequalizers.yaml                    |  3 +++
 .../regular quotient object classifier.yaml        |  3 +++
 .../regular subobject classifier.yaml              |  3 +++
 .../catdat/data/category-properties/regular.yaml   |  3 +++
 .../category-properties/right cancellative.yaml    |  3 +++
 .../catdat/data/category-properties/self-dual.yaml |  3 +++
 .../semi-strongly connected.yaml                   |  3 +++
 .../category-properties/sequential colimits.yaml   |  3 +++
 .../category-properties/sequential limits.yaml     |  3 +++
 .../data/category-properties/sifted colimits.yaml  |  3 +++
 .../catdat/data/category-properties/sifted.yaml    |  3 +++
 .../catdat/data/category-properties/skeletal.yaml  |  4 ++++
 .../catdat/data/category-properties/small.yaml     |  4 ++++
 .../data/category-properties/split abelian.yaml    |  3 +++
 .../category-properties/strict initial object.yaml |  4 ++++
 .../strict terminal object.yaml                    |  4 ++++
 .../category-properties/strongly connected.yaml    |  3 +++
 .../category-properties/subobject classifier.yaml  |  3 +++
 .../category-properties/subobject-trivial.yaml     |  3 +++
 .../data/category-properties/terminal object.yaml  |  3 +++
 .../catdat/data/category-properties/thin.yaml      |  3 +++
 .../catdat/data/category-properties/trivial.yaml   |  3 +++
 .../catdat/data/category-properties/unital.yaml    |  3 +++
 .../data/category-properties/well-copowered.yaml   |  3 +++
 .../data/category-properties/well-powered.yaml     |  3 +++
 .../data/category-properties/wide pullbacks.yaml   |  3 +++
 .../data/category-properties/wide pushouts.yaml    |  3 +++
 .../data/category-properties/zero morphisms.yaml   |  3 +++
 databases/catdat/data/config.yaml                  | 14 +++++++++++++-
 src/pages/PropertyPage.svelte                      |  5 ++++-
 173 files changed, 558 insertions(+), 2 deletions(-)

diff --git a/.cspell.json b/.cspell.json
index 8d7ec4c2e..ba45cc2ce 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -26,6 +26,7 @@
 		"abelianize",
 		"Adamek",
 		"adic",
+		"algebraicity",
 		"algébriques",
 		"anneaux",
 		"Artin",
diff --git a/databases/catdat/data/category-properties/Barr-coexact.yaml b/databases/catdat/data/category-properties/Barr-coexact.yaml
index d7893c07d..baa37126e 100644
--- a/databases/catdat/data/category-properties/Barr-coexact.yaml
+++ b/databases/catdat/data/category-properties/Barr-coexact.yaml
@@ -8,3 +8,7 @@ related_properties:
   - coregular
   - effective cocongruences
   - coquotients of cocongruences
+
+tags:
+  - limit–colimit interaction
+  - congruences
diff --git a/databases/catdat/data/category-properties/Barr-exact.yaml b/databases/catdat/data/category-properties/Barr-exact.yaml
index b0506a52f..2a0e2057b 100644
--- a/databases/catdat/data/category-properties/Barr-exact.yaml
+++ b/databases/catdat/data/category-properties/Barr-exact.yaml
@@ -10,3 +10,7 @@ related_properties:
   - effective congruences
   - quotients of congruences
   - pretopos
+
+tags:
+  - limit–colimit interaction
+  - congruences
diff --git a/databases/catdat/data/category-properties/CIP.yaml b/databases/catdat/data/category-properties/CIP.yaml
index b83f0a875..39d635eb7 100644
--- a/databases/catdat/data/category-properties/CIP.yaml
+++ b/databases/catdat/data/category-properties/CIP.yaml
@@ -14,3 +14,6 @@ related_properties:
   - filtered-colimit-stable monomorphisms
   - products
   - zero morphisms
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/CSP.yaml b/databases/catdat/data/category-properties/CSP.yaml
index 0696c77b1..261a94511 100644
--- a/databases/catdat/data/category-properties/CSP.yaml
+++ b/databases/catdat/data/category-properties/CSP.yaml
@@ -14,3 +14,6 @@ related_properties:
   - products
   - unital
   - zero morphisms
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/Cauchy complete.yaml b/databases/catdat/data/category-properties/Cauchy complete.yaml
index ed0336856..124c7b4dc 100644
--- a/databases/catdat/data/category-properties/Cauchy complete.yaml	
+++ b/databases/catdat/data/category-properties/Cauchy complete.yaml	
@@ -7,3 +7,8 @@ invariant_under_equivalences: true
 
 related_properties:
   - finitely complete
+
+tags:
+  - limits
+  - colimits
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/Grothendieck abelian.yaml b/databases/catdat/data/category-properties/Grothendieck abelian.yaml
index f5153f09c..acb702eba 100644
--- a/databases/catdat/data/category-properties/Grothendieck abelian.yaml	
+++ b/databases/catdat/data/category-properties/Grothendieck abelian.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - cocomplete
   - exact filtered colimits
   - generator
+
+tags:
+  - abelian
diff --git a/databases/catdat/data/category-properties/Grothendieck topos.yaml b/databases/catdat/data/category-properties/Grothendieck topos.yaml
index 6c05d94ae..b0af0b4fb 100644
--- a/databases/catdat/data/category-properties/Grothendieck topos.yaml	
+++ b/databases/catdat/data/category-properties/Grothendieck topos.yaml	
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - elementary topos
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/Malcev.yaml b/databases/catdat/data/category-properties/Malcev.yaml
index 72046f476..bc0686ec5 100644
--- a/databases/catdat/data/category-properties/Malcev.yaml
+++ b/databases/catdat/data/category-properties/Malcev.yaml
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - finitely complete
+
+tags:
+  - congruences
diff --git a/databases/catdat/data/category-properties/abelian.yaml b/databases/catdat/data/category-properties/abelian.yaml
index 158b2d52c..9e7ef0adb 100644
--- a/databases/catdat/data/category-properties/abelian.yaml
+++ b/databases/catdat/data/category-properties/abelian.yaml
@@ -11,3 +11,8 @@ related_properties:
   - conormal
   - kernels
   - normal
+  - Grothendieck abelian
+  - split abelian
+
+tags:
+  - abelian
diff --git a/databases/catdat/data/category-properties/accessible.yaml b/databases/catdat/data/category-properties/accessible.yaml
index 90ad9c338..1478031bc 100644
--- a/databases/catdat/data/category-properties/accessible.yaml
+++ b/databases/catdat/data/category-properties/accessible.yaml
@@ -11,3 +11,6 @@ related_properties:
   - locally poly-presentable
   - locally presentable
   - ℵ₁-accessible
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/additive.yaml b/databases/catdat/data/category-properties/additive.yaml
index 3ea1196bf..25e871f17 100644
--- a/databases/catdat/data/category-properties/additive.yaml
+++ b/databases/catdat/data/category-properties/additive.yaml
@@ -10,3 +10,9 @@ related_properties:
   - finite coproducts
   - finite products
   - preadditive
+
+tags:
+  - morphism behavior
+  - limits
+  - colimits
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/aleph1-accessible.yaml b/databases/catdat/data/category-properties/aleph1-accessible.yaml
index 6b3d96c25..fd3b3bb00 100644
--- a/databases/catdat/data/category-properties/aleph1-accessible.yaml
+++ b/databases/catdat/data/category-properties/aleph1-accessible.yaml
@@ -9,3 +9,6 @@ related_properties:
   - finitely accessible
   - locally ℵ₁-presentable
   - ℵ₁-filtered colimits
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/aleph1-cofiltered limits.yaml b/databases/catdat/data/category-properties/aleph1-cofiltered limits.yaml
index 133f5fba4..ad22cad35 100644
--- a/databases/catdat/data/category-properties/aleph1-cofiltered limits.yaml	
+++ b/databases/catdat/data/category-properties/aleph1-cofiltered limits.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - complete
   - cofiltered limits
   - ℵ₁-cofiltered
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/aleph1-cofiltered.yaml b/databases/catdat/data/category-properties/aleph1-cofiltered.yaml
index 74940bc50..8d81158f8 100644
--- a/databases/catdat/data/category-properties/aleph1-cofiltered.yaml
+++ b/databases/catdat/data/category-properties/aleph1-cofiltered.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - cofiltered
   - complete
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/aleph1-filtered colimits.yaml b/databases/catdat/data/category-properties/aleph1-filtered colimits.yaml
index 2dfd565a0..0fe02dc10 100644
--- a/databases/catdat/data/category-properties/aleph1-filtered colimits.yaml	
+++ b/databases/catdat/data/category-properties/aleph1-filtered colimits.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - filtered colimits
   - ℵ₁-accessible
   - ℵ₁-filtered
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/aleph1-filtered.yaml b/databases/catdat/data/category-properties/aleph1-filtered.yaml
index f0d2b923d..396fabfab 100644
--- a/databases/catdat/data/category-properties/aleph1-filtered.yaml
+++ b/databases/catdat/data/category-properties/aleph1-filtered.yaml
@@ -9,3 +9,6 @@ related_properties:
   - filtered
   - ℵ₁-filtered colimits
   - cocomplete
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/aleph2-small copowers.yaml b/databases/catdat/data/category-properties/aleph2-small copowers.yaml
index cb7ed4cdb..288d83834 100644
--- a/databases/catdat/data/category-properties/aleph2-small copowers.yaml	
+++ b/databases/catdat/data/category-properties/aleph2-small copowers.yaml	
@@ -12,3 +12,6 @@ related_properties:
   - countable copowers
   - finite copowers
   - ℵ₂-small coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/aleph2-small coproducts.yaml b/databases/catdat/data/category-properties/aleph2-small coproducts.yaml
index 9462a735c..841091220 100644
--- a/databases/catdat/data/category-properties/aleph2-small coproducts.yaml	
+++ b/databases/catdat/data/category-properties/aleph2-small coproducts.yaml	
@@ -12,3 +12,6 @@ related_properties:
   - countable coproducts
   - finite coproducts
   - ℵ₂-small powers
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/aleph2-small powers.yaml b/databases/catdat/data/category-properties/aleph2-small powers.yaml
index 76a30ebbc..c7fed3551 100644
--- a/databases/catdat/data/category-properties/aleph2-small powers.yaml	
+++ b/databases/catdat/data/category-properties/aleph2-small powers.yaml	
@@ -12,3 +12,6 @@ related_properties:
   - countable powers
   - finite powers
   - ℵ₂-small products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/aleph2-small products.yaml b/databases/catdat/data/category-properties/aleph2-small products.yaml
index 09c3e43b2..a36be0408 100644
--- a/databases/catdat/data/category-properties/aleph2-small products.yaml	
+++ b/databases/catdat/data/category-properties/aleph2-small products.yaml	
@@ -12,3 +12,6 @@ related_properties:
   - countable products
   - finite products
   - ℵ₂-small powers
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/balanced.yaml b/databases/catdat/data/category-properties/balanced.yaml
index b2bda4732..d093f4778 100644
--- a/databases/catdat/data/category-properties/balanced.yaml
+++ b/databases/catdat/data/category-properties/balanced.yaml
@@ -6,3 +6,6 @@ dual_property: balanced
 invariant_under_equivalences: true
 
 related_properties: []
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/binary copowers.yaml b/databases/catdat/data/category-properties/binary copowers.yaml
index e37ff743c..ea47d319b 100644
--- a/databases/catdat/data/category-properties/binary copowers.yaml	
+++ b/databases/catdat/data/category-properties/binary copowers.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite copowers
   - finite coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/binary coproducts.yaml b/databases/catdat/data/category-properties/binary coproducts.yaml
index 46376fd22..57ad9323a 100644
--- a/databases/catdat/data/category-properties/binary coproducts.yaml	
+++ b/databases/catdat/data/category-properties/binary coproducts.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - binary copowers
   - finite coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/binary powers.yaml b/databases/catdat/data/category-properties/binary powers.yaml
index b93171974..7d736621d 100644
--- a/databases/catdat/data/category-properties/binary powers.yaml	
+++ b/databases/catdat/data/category-properties/binary powers.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite powers
   - finite products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/binary products.yaml b/databases/catdat/data/category-properties/binary products.yaml
index fabae3e25..9c2136e48 100644
--- a/databases/catdat/data/category-properties/binary products.yaml	
+++ b/databases/catdat/data/category-properties/binary products.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - binary powers
   - finite products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/biproducts.yaml b/databases/catdat/data/category-properties/biproducts.yaml
index 9d5f5511a..6f37d9f23 100644
--- a/databases/catdat/data/category-properties/biproducts.yaml
+++ b/databases/catdat/data/category-properties/biproducts.yaml
@@ -13,3 +13,8 @@ related_properties:
   - finite coproducts
   - finite products
   - zero morphisms
+
+tags:
+  - limits
+  - colimits
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/cartesian closed.yaml b/databases/catdat/data/category-properties/cartesian closed.yaml
index 18fc27dff..f7cbe31e2 100644
--- a/databases/catdat/data/category-properties/cartesian closed.yaml	
+++ b/databases/catdat/data/category-properties/cartesian closed.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite products
   - locally cartesian closed
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/cartesian filtered colimits.yaml b/databases/catdat/data/category-properties/cartesian filtered colimits.yaml
index 519928b72..6bff1f0a2 100644
--- a/databases/catdat/data/category-properties/cartesian filtered colimits.yaml	
+++ b/databases/catdat/data/category-properties/cartesian filtered colimits.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - exact filtered colimits
   - filtered colimits
   - finite products
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/co-Malcev.yaml b/databases/catdat/data/category-properties/co-Malcev.yaml
index d3c56a896..f63ddc049 100644
--- a/databases/catdat/data/category-properties/co-Malcev.yaml
+++ b/databases/catdat/data/category-properties/co-Malcev.yaml
@@ -9,3 +9,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - finitely cocomplete
+
+tags:
+  - congruences
diff --git a/databases/catdat/data/category-properties/coaccessible.yaml b/databases/catdat/data/category-properties/coaccessible.yaml
index ef434d950..26aadf482 100644
--- a/databases/catdat/data/category-properties/coaccessible.yaml
+++ b/databases/catdat/data/category-properties/coaccessible.yaml
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - locally copresentable
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/cocartesian coclosed.yaml b/databases/catdat/data/category-properties/cocartesian coclosed.yaml
index dd20312b7..bd89b6bae 100644
--- a/databases/catdat/data/category-properties/cocartesian coclosed.yaml	
+++ b/databases/catdat/data/category-properties/cocartesian coclosed.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite coproducts
   - locally cocartesian coclosed
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/cocartesian cofiltered limits.yaml b/databases/catdat/data/category-properties/cocartesian cofiltered limits.yaml
index be2cdc96e..b4eabfece 100644
--- a/databases/catdat/data/category-properties/cocartesian cofiltered limits.yaml	
+++ b/databases/catdat/data/category-properties/cocartesian cofiltered limits.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - cofiltered limits
   - exact cofiltered limits
   - finite coproducts
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/cocomplete.yaml b/databases/catdat/data/category-properties/cocomplete.yaml
index 487bd32b8..cc946755b 100644
--- a/databases/catdat/data/category-properties/cocomplete.yaml
+++ b/databases/catdat/data/category-properties/cocomplete.yaml
@@ -9,3 +9,6 @@ related_properties:
   - coequalizers
   - coproducts
   - multi-cocomplete
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/codistributive.yaml b/databases/catdat/data/category-properties/codistributive.yaml
index 2f7dd68d3..120ed44b7 100644
--- a/databases/catdat/data/category-properties/codistributive.yaml
+++ b/databases/catdat/data/category-properties/codistributive.yaml
@@ -9,3 +9,6 @@ related_properties:
   - finite coproducts
   - finite products
   - infinitary codistributive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/coequalizers.yaml b/databases/catdat/data/category-properties/coequalizers.yaml
index d09e6c159..668192eb0 100644
--- a/databases/catdat/data/category-properties/coequalizers.yaml
+++ b/databases/catdat/data/category-properties/coequalizers.yaml
@@ -10,3 +10,6 @@ related_properties:
   - finitely cocomplete
   - quotients of congruences
   - reflexive coequalizers
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/coextensive.yaml b/databases/catdat/data/category-properties/coextensive.yaml
index 96a0f9853..a8bfa5868 100644
--- a/databases/catdat/data/category-properties/coextensive.yaml
+++ b/databases/catdat/data/category-properties/coextensive.yaml
@@ -8,3 +8,6 @@ related_properties:
   - disjoint finite products
   - finite products
   - infinitary coextensive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/cofiltered limits.yaml b/databases/catdat/data/category-properties/cofiltered limits.yaml
index 9f8400306..c0e321d3e 100644
--- a/databases/catdat/data/category-properties/cofiltered limits.yaml	
+++ b/databases/catdat/data/category-properties/cofiltered limits.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - complete
   - cosifted limits
   - directed limits
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/cofiltered-limit-stable epimorphisms.yaml b/databases/catdat/data/category-properties/cofiltered-limit-stable epimorphisms.yaml
index dca205851..27e6dd064 100644
--- a/databases/catdat/data/category-properties/cofiltered-limit-stable epimorphisms.yaml	
+++ b/databases/catdat/data/category-properties/cofiltered-limit-stable epimorphisms.yaml	
@@ -7,3 +7,7 @@ invariant_under_equivalences: true
 related_properties:
   - cofiltered limits
   - exact cofiltered limits
+
+tags:
+  - morphism behavior
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/cofiltered.yaml b/databases/catdat/data/category-properties/cofiltered.yaml
index c0f4dc191..75fada8d5 100644
--- a/databases/catdat/data/category-properties/cofiltered.yaml
+++ b/databases/catdat/data/category-properties/cofiltered.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - cofiltered limits
   - finitely complete
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/cogenerating set.yaml b/databases/catdat/data/category-properties/cogenerating set.yaml
index 73bac907a..d894b6263 100644
--- a/databases/catdat/data/category-properties/cogenerating set.yaml	
+++ b/databases/catdat/data/category-properties/cogenerating set.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - cogenerator
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/cogenerator.yaml b/databases/catdat/data/category-properties/cogenerator.yaml
index e111ba140..b1ae65495 100644
--- a/databases/catdat/data/category-properties/cogenerator.yaml
+++ b/databases/catdat/data/category-properties/cogenerator.yaml
@@ -7,3 +7,7 @@ invariant_under_equivalences: true
 
 related_properties:
   - cogenerating set
+
+tags:
+  - morphism behavior
+  - size
diff --git a/databases/catdat/data/category-properties/cokernels.yaml b/databases/catdat/data/category-properties/cokernels.yaml
index 492822227..203b3ab7b 100644
--- a/databases/catdat/data/category-properties/cokernels.yaml
+++ b/databases/catdat/data/category-properties/cokernels.yaml
@@ -10,3 +10,6 @@ related_properties:
   - conormal
   - quotients of congruences
   - zero morphisms
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/complete.yaml b/databases/catdat/data/category-properties/complete.yaml
index 9b164df56..a006f4291 100644
--- a/databases/catdat/data/category-properties/complete.yaml
+++ b/databases/catdat/data/category-properties/complete.yaml
@@ -9,3 +9,6 @@ related_properties:
   - equalizers
   - multi-complete
   - products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/connected colimits.yaml b/databases/catdat/data/category-properties/connected colimits.yaml
index c1b0328ff..31330c042 100644
--- a/databases/catdat/data/category-properties/connected colimits.yaml	
+++ b/databases/catdat/data/category-properties/connected colimits.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - cocomplete
   - connected
   - filtered colimits
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/connected limits.yaml b/databases/catdat/data/category-properties/connected limits.yaml
index 3a4f36bf3..34bb8d0c5 100644
--- a/databases/catdat/data/category-properties/connected limits.yaml	
+++ b/databases/catdat/data/category-properties/connected limits.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - cofiltered limits
   - complete
   - connected
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/connected.yaml b/databases/catdat/data/category-properties/connected.yaml
index 8d8a8eb46..aa9bb04f3 100644
--- a/databases/catdat/data/category-properties/connected.yaml
+++ b/databases/catdat/data/category-properties/connected.yaml
@@ -9,3 +9,6 @@ related_properties:
   - inhabited
   - semi-strongly connected
   - strongly connected
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/conormal.yaml b/databases/catdat/data/category-properties/conormal.yaml
index 97855b149..fe3f0bb68 100644
--- a/databases/catdat/data/category-properties/conormal.yaml
+++ b/databases/catdat/data/category-properties/conormal.yaml
@@ -10,3 +10,6 @@ related_properties:
   - effective cocongruences
   - epi-regular
   - zero morphisms
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/copowers.yaml b/databases/catdat/data/category-properties/copowers.yaml
index e47a319ea..1bf851b37 100644
--- a/databases/catdat/data/category-properties/copowers.yaml
+++ b/databases/catdat/data/category-properties/copowers.yaml
@@ -9,3 +9,6 @@ related_properties:
   - coproducts
   - countable copowers
   - finite copowers
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/coproducts.yaml b/databases/catdat/data/category-properties/coproducts.yaml
index dd948e8be..63280a7bd 100644
--- a/databases/catdat/data/category-properties/coproducts.yaml
+++ b/databases/catdat/data/category-properties/coproducts.yaml
@@ -9,3 +9,6 @@ related_properties:
   - cocomplete
   - copowers
   - finite coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/coquotients of cocongruences.yaml b/databases/catdat/data/category-properties/coquotients of cocongruences.yaml
index 2bf9b64a1..3dbf88a59 100644
--- a/databases/catdat/data/category-properties/coquotients of cocongruences.yaml	
+++ b/databases/catdat/data/category-properties/coquotients of cocongruences.yaml	
@@ -10,3 +10,7 @@ related_properties:
   - equalizers
   - kernels
   - Barr-coexact
+
+tags:
+  - limits
+  - congruences
diff --git a/databases/catdat/data/category-properties/core-thin.yaml b/databases/catdat/data/category-properties/core-thin.yaml
index 111407dc5..9f584fa86 100644
--- a/databases/catdat/data/category-properties/core-thin.yaml
+++ b/databases/catdat/data/category-properties/core-thin.yaml
@@ -15,3 +15,6 @@ related_properties:
   - gaunt
   - one-way
   - thin
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/coreflexive equalizers.yaml b/databases/catdat/data/category-properties/coreflexive equalizers.yaml
index 1508fc34c..91fc82763 100644
--- a/databases/catdat/data/category-properties/coreflexive equalizers.yaml	
+++ b/databases/catdat/data/category-properties/coreflexive equalizers.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - cosifted limits
   - equalizers
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/coregular.yaml b/databases/catdat/data/category-properties/coregular.yaml
index ed9d719d1..c40be8b33 100644
--- a/databases/catdat/data/category-properties/coregular.yaml
+++ b/databases/catdat/data/category-properties/coregular.yaml
@@ -8,3 +8,6 @@ related_properties:
   - coquotients of cocongruences
   - finitely cocomplete
   - Barr-coexact
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/cosifted limits.yaml b/databases/catdat/data/category-properties/cosifted limits.yaml
index ba0314e9d..19bf53019 100644
--- a/databases/catdat/data/category-properties/cosifted limits.yaml	
+++ b/databases/catdat/data/category-properties/cosifted limits.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - complete
   - coreflexive equalizers
   - cosifted
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/cosifted.yaml b/databases/catdat/data/category-properties/cosifted.yaml
index ac78af886..6f4dd59e3 100644
--- a/databases/catdat/data/category-properties/cosifted.yaml
+++ b/databases/catdat/data/category-properties/cosifted.yaml
@@ -9,3 +9,6 @@ related_properties:
   - cofiltered
   - connected
   - cosifted limits
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/counital.yaml b/databases/catdat/data/category-properties/counital.yaml
index 57e443b74..4ad028876 100644
--- a/databases/catdat/data/category-properties/counital.yaml
+++ b/databases/catdat/data/category-properties/counital.yaml
@@ -8,3 +8,6 @@ related_properties:
   - co-Malcev
   - finitely cocomplete
   - pointed
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/countable copowers.yaml b/databases/catdat/data/category-properties/countable copowers.yaml
index a45af75a8..cab9fd83c 100644
--- a/databases/catdat/data/category-properties/countable copowers.yaml	
+++ b/databases/catdat/data/category-properties/countable copowers.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - countable coproducts
   - finite copowers
   - ℵ₂-small copowers
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/countable coproducts.yaml b/databases/catdat/data/category-properties/countable coproducts.yaml
index 8a6c10c09..78235f27e 100644
--- a/databases/catdat/data/category-properties/countable coproducts.yaml	
+++ b/databases/catdat/data/category-properties/countable coproducts.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - finite coproducts
   - countable copowers
   - ℵ₂-small coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/countable powers.yaml b/databases/catdat/data/category-properties/countable powers.yaml
index 44d26e1c0..0a0e36510 100644
--- a/databases/catdat/data/category-properties/countable powers.yaml	
+++ b/databases/catdat/data/category-properties/countable powers.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - finite powers
   - powers
   - ℵ₂-small powers
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/countable products.yaml b/databases/catdat/data/category-properties/countable products.yaml
index 390a0b157..09143a503 100644
--- a/databases/catdat/data/category-properties/countable products.yaml	
+++ b/databases/catdat/data/category-properties/countable products.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - finite products
   - countable powers
   - ℵ₂-small products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/countable.yaml b/databases/catdat/data/category-properties/countable.yaml
index 4c0ef80ae..45043fd30 100644
--- a/databases/catdat/data/category-properties/countable.yaml
+++ b/databases/catdat/data/category-properties/countable.yaml
@@ -7,3 +7,7 @@ invariant_under_equivalences: false
 related_properties:
   - essentially countable
   - finite
+
+tags:
+  - size
+  - evil
diff --git a/databases/catdat/data/category-properties/countably codistributive.yaml b/databases/catdat/data/category-properties/countably codistributive.yaml
index 90ac5e0ae..7dd545865 100644
--- a/databases/catdat/data/category-properties/countably codistributive.yaml	
+++ b/databases/catdat/data/category-properties/countably codistributive.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - countable products
   - finite coproducts
   - infinitary codistributive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/countably distributive.yaml b/databases/catdat/data/category-properties/countably distributive.yaml
index b4b0d85d8..77a97ba9b 100644
--- a/databases/catdat/data/category-properties/countably distributive.yaml	
+++ b/databases/catdat/data/category-properties/countably distributive.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - distributive
   - finite products
   - infinitary distributive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/direct.yaml b/databases/catdat/data/category-properties/direct.yaml
index eb66caa25..9ddff627c 100644
--- a/databases/catdat/data/category-properties/direct.yaml
+++ b/databases/catdat/data/category-properties/direct.yaml
@@ -11,3 +11,7 @@ invariant_under_equivalences: false
 related_properties:
   - one-way
   - skeletal
+
+tags:
+  - morphism behavior
+  - evil
diff --git a/databases/catdat/data/category-properties/directed colimits.yaml b/databases/catdat/data/category-properties/directed colimits.yaml
index 531cf3884..68cb73fd7 100644
--- a/databases/catdat/data/category-properties/directed colimits.yaml	
+++ b/databases/catdat/data/category-properties/directed colimits.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - cocomplete
   - filtered colimits
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/directed limits.yaml b/databases/catdat/data/category-properties/directed limits.yaml
index 7d1d96659..61ff31f38 100644
--- a/databases/catdat/data/category-properties/directed limits.yaml	
+++ b/databases/catdat/data/category-properties/directed limits.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - cofiltered limits
   - complete
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/discrete.yaml b/databases/catdat/data/category-properties/discrete.yaml
index 01a1a28bf..8a3f31bc0 100644
--- a/databases/catdat/data/category-properties/discrete.yaml
+++ b/databases/catdat/data/category-properties/discrete.yaml
@@ -8,3 +8,7 @@ invariant_under_equivalences: false
 related_properties:
   - essentially discrete
   - thin
+
+tags:
+  - morphism behavior
+  - evil
diff --git a/databases/catdat/data/category-properties/disjoint coproducts.yaml b/databases/catdat/data/category-properties/disjoint coproducts.yaml
index 1e864a92d..01532e0b2 100644
--- a/databases/catdat/data/category-properties/disjoint coproducts.yaml	
+++ b/databases/catdat/data/category-properties/disjoint coproducts.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - coproducts
   - disjoint finite coproducts
   - infinitary extensive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/disjoint finite coproducts.yaml b/databases/catdat/data/category-properties/disjoint finite coproducts.yaml
index cbae37fa9..1a1ad8457 100644
--- a/databases/catdat/data/category-properties/disjoint finite coproducts.yaml	
+++ b/databases/catdat/data/category-properties/disjoint finite coproducts.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - disjoint coproducts
   - extensive
   - finite coproducts
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/disjoint finite products.yaml b/databases/catdat/data/category-properties/disjoint finite products.yaml
index 899648cad..892a0c821 100644
--- a/databases/catdat/data/category-properties/disjoint finite products.yaml	
+++ b/databases/catdat/data/category-properties/disjoint finite products.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - coextensive
   - disjoint products
   - finite products
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/disjoint products.yaml b/databases/catdat/data/category-properties/disjoint products.yaml
index 75e6cdc2a..cddf08e9b 100644
--- a/databases/catdat/data/category-properties/disjoint products.yaml	
+++ b/databases/catdat/data/category-properties/disjoint products.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - disjoint finite products
   - infinitary coextensive
   - products
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/distributive.yaml b/databases/catdat/data/category-properties/distributive.yaml
index e2a491266..e8e815515 100644
--- a/databases/catdat/data/category-properties/distributive.yaml
+++ b/databases/catdat/data/category-properties/distributive.yaml
@@ -10,3 +10,6 @@ related_properties:
   - finite coproducts
   - finite products
   - infinitary distributive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/effective cocongruences.yaml b/databases/catdat/data/category-properties/effective cocongruences.yaml
index 85c2fe42a..f72c0c637 100644
--- a/databases/catdat/data/category-properties/effective cocongruences.yaml	
+++ b/databases/catdat/data/category-properties/effective cocongruences.yaml	
@@ -12,3 +12,6 @@ related_properties:
   - coquotients of cocongruences
   - epi-regular
   - Barr-coexact
+
+tags:
+  - congruences
diff --git a/databases/catdat/data/category-properties/effective congruences.yaml b/databases/catdat/data/category-properties/effective congruences.yaml
index ed2ecc2e4..4106c9403 100644
--- a/databases/catdat/data/category-properties/effective congruences.yaml	
+++ b/databases/catdat/data/category-properties/effective congruences.yaml	
@@ -13,3 +13,6 @@ related_properties:
   - normal
   - quotients of congruences
   - Barr-exact
+
+tags:
+  - congruences
diff --git a/databases/catdat/data/category-properties/elementary topos.yaml b/databases/catdat/data/category-properties/elementary topos.yaml
index 5686a0f45..e82694011 100644
--- a/databases/catdat/data/category-properties/elementary topos.yaml	
+++ b/databases/catdat/data/category-properties/elementary topos.yaml	
@@ -11,3 +11,6 @@ related_properties:
   - natural numbers object
   - subobject classifier
   - pretopos
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/epi-regular.yaml b/databases/catdat/data/category-properties/epi-regular.yaml
index 91d0b17a7..5f78a36ea 100644
--- a/databases/catdat/data/category-properties/epi-regular.yaml
+++ b/databases/catdat/data/category-properties/epi-regular.yaml
@@ -9,3 +9,6 @@ related_properties:
   - conormal
   - effective cocongruences
   - quotient-trivial
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/equalizers.yaml b/databases/catdat/data/category-properties/equalizers.yaml
index a7e56e300..5d6bf2565 100644
--- a/databases/catdat/data/category-properties/equalizers.yaml
+++ b/databases/catdat/data/category-properties/equalizers.yaml
@@ -10,3 +10,6 @@ related_properties:
   - coreflexive equalizers
   - finitely complete
   - kernels
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/essentially countable.yaml b/databases/catdat/data/category-properties/essentially countable.yaml
index 39d041455..a7fd7f2b3 100644
--- a/databases/catdat/data/category-properties/essentially countable.yaml	
+++ b/databases/catdat/data/category-properties/essentially countable.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 related_properties:
   - countable
   - essentially finite
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/essentially discrete.yaml b/databases/catdat/data/category-properties/essentially discrete.yaml
index e81567f74..130c00bb9 100644
--- a/databases/catdat/data/category-properties/essentially discrete.yaml	
+++ b/databases/catdat/data/category-properties/essentially discrete.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - discrete
   - thin
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/essentially finite.yaml b/databases/catdat/data/category-properties/essentially finite.yaml
index 0323dfa68..140bda0fb 100644
--- a/databases/catdat/data/category-properties/essentially finite.yaml	
+++ b/databases/catdat/data/category-properties/essentially finite.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - essentially small
   - finite
   - locally finite
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/essentially small.yaml b/databases/catdat/data/category-properties/essentially small.yaml
index 10e292a96..5cdd12d76 100644
--- a/databases/catdat/data/category-properties/essentially small.yaml	
+++ b/databases/catdat/data/category-properties/essentially small.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - locally essentially small
   - small
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/exact cofiltered limits.yaml b/databases/catdat/data/category-properties/exact cofiltered limits.yaml
index 34a63abcd..cc52e5193 100644
--- a/databases/catdat/data/category-properties/exact cofiltered limits.yaml	
+++ b/databases/catdat/data/category-properties/exact cofiltered limits.yaml	
@@ -16,3 +16,6 @@ related_properties:
   - cofiltered limits
   - cofiltered-limit-stable epimorphisms
   - finitely cocomplete
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/exact filtered colimits.yaml b/databases/catdat/data/category-properties/exact filtered colimits.yaml
index 8d83e983e..2cd2993b0 100644
--- a/databases/catdat/data/category-properties/exact filtered colimits.yaml	
+++ b/databases/catdat/data/category-properties/exact filtered colimits.yaml	
@@ -15,3 +15,6 @@ related_properties:
   - cartesian filtered colimits
   - filtered colimits
   - finitely complete
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/extensive.yaml b/databases/catdat/data/category-properties/extensive.yaml
index c95604b9f..9fc3fb09e 100644
--- a/databases/catdat/data/category-properties/extensive.yaml
+++ b/databases/catdat/data/category-properties/extensive.yaml
@@ -10,3 +10,6 @@ related_properties:
   - finite coproducts
   - infinitary extensive
   - pretopos
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/filtered colimits.yaml b/databases/catdat/data/category-properties/filtered colimits.yaml
index 9cc8bc4f4..02c5550d6 100644
--- a/databases/catdat/data/category-properties/filtered colimits.yaml	
+++ b/databases/catdat/data/category-properties/filtered colimits.yaml	
@@ -11,3 +11,6 @@ related_properties:
   - filtered
   - sifted colimits
   - ℵ₁-filtered colimits
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/filtered-colimit-stable monomorphisms.yaml b/databases/catdat/data/category-properties/filtered-colimit-stable monomorphisms.yaml
index d3c18515c..d63a823e6 100644
--- a/databases/catdat/data/category-properties/filtered-colimit-stable monomorphisms.yaml	
+++ b/databases/catdat/data/category-properties/filtered-colimit-stable monomorphisms.yaml	
@@ -7,3 +7,7 @@ invariant_under_equivalences: true
 related_properties:
   - exact filtered colimits
   - filtered colimits
+
+tags:
+  - morphism behavior
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/filtered.yaml b/databases/catdat/data/category-properties/filtered.yaml
index 7ce6254b5..5ecbcda57 100644
--- a/databases/catdat/data/category-properties/filtered.yaml
+++ b/databases/catdat/data/category-properties/filtered.yaml
@@ -10,3 +10,6 @@ related_properties:
   - filtered colimits
   - cocomplete
   - sifted
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/finitary algebraic.yaml b/databases/catdat/data/category-properties/finitary algebraic.yaml
index 1ab6ad299..b94b6abb5 100644
--- a/databases/catdat/data/category-properties/finitary algebraic.yaml	
+++ b/databases/catdat/data/category-properties/finitary algebraic.yaml	
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - locally strongly finitely presentable
+
+tags:
+  - algebraicity
diff --git a/databases/catdat/data/category-properties/finite copowers.yaml b/databases/catdat/data/category-properties/finite copowers.yaml
index e662ba435..7d5c8857d 100644
--- a/databases/catdat/data/category-properties/finite copowers.yaml	
+++ b/databases/catdat/data/category-properties/finite copowers.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - copowers
   - countable copowers
   - finite coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/finite coproducts.yaml b/databases/catdat/data/category-properties/finite coproducts.yaml
index 76b342f69..bff4b4938 100644
--- a/databases/catdat/data/category-properties/finite coproducts.yaml	
+++ b/databases/catdat/data/category-properties/finite coproducts.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - coproducts
   - finite copowers
   - initial object
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/finite powers.yaml b/databases/catdat/data/category-properties/finite powers.yaml
index 0f06315a2..c5617984e 100644
--- a/databases/catdat/data/category-properties/finite powers.yaml	
+++ b/databases/catdat/data/category-properties/finite powers.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - countable powers
   - finite products
   - powers
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/finite products.yaml b/databases/catdat/data/category-properties/finite products.yaml
index fbcc86708..3a5730078 100644
--- a/databases/catdat/data/category-properties/finite products.yaml	
+++ b/databases/catdat/data/category-properties/finite products.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - finite powers
   - products
   - terminal object
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/finite.yaml b/databases/catdat/data/category-properties/finite.yaml
index b7a9e792b..04eb1ca93 100644
--- a/databases/catdat/data/category-properties/finite.yaml
+++ b/databases/catdat/data/category-properties/finite.yaml
@@ -10,3 +10,7 @@ related_properties:
   - essentially finite
   - locally finite
   - small
+
+tags:
+  - size
+  - evil
diff --git a/databases/catdat/data/category-properties/finitely accessible.yaml b/databases/catdat/data/category-properties/finitely accessible.yaml
index f162330e3..afdaf8685 100644
--- a/databases/catdat/data/category-properties/finitely accessible.yaml	
+++ b/databases/catdat/data/category-properties/finitely accessible.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - locally finitely multi-presentable
   - locally finitely presentable
   - ℵ₁-accessible
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/finitely cocomplete.yaml b/databases/catdat/data/category-properties/finitely cocomplete.yaml
index 593348d61..91c0088e4 100644
--- a/databases/catdat/data/category-properties/finitely cocomplete.yaml	
+++ b/databases/catdat/data/category-properties/finitely cocomplete.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - cocomplete
   - coequalizers
   - finite coproducts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/finitely complete.yaml b/databases/catdat/data/category-properties/finitely complete.yaml
index 932f2a449..c8e5aeec8 100644
--- a/databases/catdat/data/category-properties/finitely complete.yaml	
+++ b/databases/catdat/data/category-properties/finitely complete.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - complete
   - equalizers
   - finite products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/gaunt.yaml b/databases/catdat/data/category-properties/gaunt.yaml
index 563bc17c5..d2378205a 100644
--- a/databases/catdat/data/category-properties/gaunt.yaml
+++ b/databases/catdat/data/category-properties/gaunt.yaml
@@ -9,3 +9,7 @@ related_properties:
   - core-thin
   - one-way
   - skeletal
+
+tags:
+  - morphism behavior
+  - evil
diff --git a/databases/catdat/data/category-properties/generalized variety.yaml b/databases/catdat/data/category-properties/generalized variety.yaml
index a7be520d9..96d4245d1 100644
--- a/databases/catdat/data/category-properties/generalized variety.yaml	
+++ b/databases/catdat/data/category-properties/generalized variety.yaml	
@@ -7,3 +7,6 @@ related_properties:
   - locally strongly finitely presentable
   - multi-algebraic
   - sifted colimits
+
+tags:
+  - algebraicity
diff --git a/databases/catdat/data/category-properties/generating set.yaml b/databases/catdat/data/category-properties/generating set.yaml
index 4588065ca..a815ea45e 100644
--- a/databases/catdat/data/category-properties/generating set.yaml	
+++ b/databases/catdat/data/category-properties/generating set.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - generator
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/generator.yaml b/databases/catdat/data/category-properties/generator.yaml
index 51b95d34e..14b3b3af9 100644
--- a/databases/catdat/data/category-properties/generator.yaml
+++ b/databases/catdat/data/category-properties/generator.yaml
@@ -7,3 +7,7 @@ invariant_under_equivalences: true
 
 related_properties:
   - generating set
+
+tags:
+  - morphism behavior
+  - size
diff --git a/databases/catdat/data/category-properties/groupoid.yaml b/databases/catdat/data/category-properties/groupoid.yaml
index 706c0dfb4..5677bbb3f 100644
--- a/databases/catdat/data/category-properties/groupoid.yaml
+++ b/databases/catdat/data/category-properties/groupoid.yaml
@@ -10,3 +10,6 @@ related_properties:
   - quotient-trivial
   - right cancellative
   - subobject-trivial
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/infinitary codistributive.yaml b/databases/catdat/data/category-properties/infinitary codistributive.yaml
index aa8d39364..681390d11 100644
--- a/databases/catdat/data/category-properties/infinitary codistributive.yaml	
+++ b/databases/catdat/data/category-properties/infinitary codistributive.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - countably codistributive
   - finite coproducts
   - products
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/infinitary coextensive.yaml b/databases/catdat/data/category-properties/infinitary coextensive.yaml
index 0af9ba6c0..0b0aa0ab0 100644
--- a/databases/catdat/data/category-properties/infinitary coextensive.yaml	
+++ b/databases/catdat/data/category-properties/infinitary coextensive.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - coextensive
   - disjoint products
   - products
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/infinitary distributive.yaml b/databases/catdat/data/category-properties/infinitary distributive.yaml
index c4388dbe0..11c75a681 100644
--- a/databases/catdat/data/category-properties/infinitary distributive.yaml	
+++ b/databases/catdat/data/category-properties/infinitary distributive.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - countably distributive
   - distributive
   - finite products
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/infinitary extensive.yaml b/databases/catdat/data/category-properties/infinitary extensive.yaml
index ca81ddecf..49d0be9cf 100644
--- a/databases/catdat/data/category-properties/infinitary extensive.yaml	
+++ b/databases/catdat/data/category-properties/infinitary extensive.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - coproducts
   - disjoint coproducts
   - extensive
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/inhabited.yaml b/databases/catdat/data/category-properties/inhabited.yaml
index 4d93cd40b..702763f9b 100644
--- a/databases/catdat/data/category-properties/inhabited.yaml
+++ b/databases/catdat/data/category-properties/inhabited.yaml
@@ -6,3 +6,6 @@ dual_property: inhabited
 invariant_under_equivalences: true
 
 related_properties: []
+
+tags:
+  - misc
diff --git a/databases/catdat/data/category-properties/initial object.yaml b/databases/catdat/data/category-properties/initial object.yaml
index e7a482bf2..0894bf5ea 100644
--- a/databases/catdat/data/category-properties/initial object.yaml	
+++ b/databases/catdat/data/category-properties/initial object.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite coproducts
   - multi-initial object
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/inverse.yaml b/databases/catdat/data/category-properties/inverse.yaml
index 766dae97f..7e999f15c 100644
--- a/databases/catdat/data/category-properties/inverse.yaml
+++ b/databases/catdat/data/category-properties/inverse.yaml
@@ -10,3 +10,7 @@ invariant_under_equivalences: false
 related_properties:
   - one-way
   - skeletal
+
+tags:
+  - morphism behavior
+  - evil
diff --git a/databases/catdat/data/category-properties/kernels.yaml b/databases/catdat/data/category-properties/kernels.yaml
index 5373d2be1..9d17da099 100644
--- a/databases/catdat/data/category-properties/kernels.yaml
+++ b/databases/catdat/data/category-properties/kernels.yaml
@@ -10,3 +10,6 @@ related_properties:
   - equalizers
   - normal
   - zero morphisms
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/left cancellative.yaml b/databases/catdat/data/category-properties/left cancellative.yaml
index ad9ce7fe8..225429aaf 100644
--- a/databases/catdat/data/category-properties/left cancellative.yaml	
+++ b/databases/catdat/data/category-properties/left cancellative.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - groupoid
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/locally aleph1-presentable.yaml b/databases/catdat/data/category-properties/locally aleph1-presentable.yaml
index 90d839f3a..0ced5cc54 100644
--- a/databases/catdat/data/category-properties/locally aleph1-presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally aleph1-presentable.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - locally finitely presentable
   - locally presentable
   - ℵ₁-accessible
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally cartesian closed.yaml b/databases/catdat/data/category-properties/locally cartesian closed.yaml
index b98679b31..a142235a4 100644
--- a/databases/catdat/data/category-properties/locally cartesian closed.yaml	
+++ b/databases/catdat/data/category-properties/locally cartesian closed.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - cartesian closed
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/locally cocartesian coclosed.yaml b/databases/catdat/data/category-properties/locally cocartesian coclosed.yaml
index f8c53e8c6..9c0ea1ac2 100644
--- a/databases/catdat/data/category-properties/locally cocartesian coclosed.yaml	
+++ b/databases/catdat/data/category-properties/locally cocartesian coclosed.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - cocartesian coclosed
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/locally copresentable.yaml b/databases/catdat/data/category-properties/locally copresentable.yaml
index 12563b17d..ef60a7d60 100644
--- a/databases/catdat/data/category-properties/locally copresentable.yaml	
+++ b/databases/catdat/data/category-properties/locally copresentable.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 related_properties:
   - coaccessible
   - complete
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally essentially small.yaml b/databases/catdat/data/category-properties/locally essentially small.yaml
index 59915cdf6..12f5480fb 100644
--- a/databases/catdat/data/category-properties/locally essentially small.yaml	
+++ b/databases/catdat/data/category-properties/locally essentially small.yaml	
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - locally small
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/locally finite.yaml b/databases/catdat/data/category-properties/locally finite.yaml
index 2b0318898..40df92788 100644
--- a/databases/catdat/data/category-properties/locally finite.yaml	
+++ b/databases/catdat/data/category-properties/locally finite.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite
   - thin
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/locally finitely multi-presentable.yaml b/databases/catdat/data/category-properties/locally finitely multi-presentable.yaml
index 6da339bd3..679baca11 100644
--- a/databases/catdat/data/category-properties/locally finitely multi-presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally finitely multi-presentable.yaml	
@@ -19,3 +19,6 @@ related_properties:
   - locally multi-presentable
   - multi-algebraic
   - multi-cocomplete
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally finitely presentable.yaml b/databases/catdat/data/category-properties/locally finitely presentable.yaml
index d1926dd31..23a818aaa 100644
--- a/databases/catdat/data/category-properties/locally finitely presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally finitely presentable.yaml	
@@ -21,3 +21,6 @@ related_properties:
   - locally presentable
   - locally strongly finitely presentable
   - locally ℵ₁-presentable
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally multi-presentable.yaml b/databases/catdat/data/category-properties/locally multi-presentable.yaml
index bb77c2ab0..7daf3b1b9 100644
--- a/databases/catdat/data/category-properties/locally multi-presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally multi-presentable.yaml	
@@ -19,3 +19,6 @@ related_properties:
   - locally poly-presentable
   - locally presentable
   - multi-cocomplete
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally poly-presentable.yaml b/databases/catdat/data/category-properties/locally poly-presentable.yaml
index 83883e7b5..1779f8cdc 100644
--- a/databases/catdat/data/category-properties/locally poly-presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally poly-presentable.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - locally multi-presentable
   - locally presentable
   - wide pullbacks
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally presentable.yaml b/databases/catdat/data/category-properties/locally presentable.yaml
index 53c681d2b..b37156a3d 100644
--- a/databases/catdat/data/category-properties/locally presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally presentable.yaml	
@@ -21,3 +21,6 @@ related_properties:
   - locally multi-presentable
   - locally poly-presentable
   - locally ℵ₁-presentable
+
+tags:
+  - accessibility
diff --git a/databases/catdat/data/category-properties/locally small.yaml b/databases/catdat/data/category-properties/locally small.yaml
index d0a386053..d767e88a2 100644
--- a/databases/catdat/data/category-properties/locally small.yaml	
+++ b/databases/catdat/data/category-properties/locally small.yaml	
@@ -8,3 +8,7 @@ invariant_under_equivalences: false
 related_properties:
   - locally essentially small
   - small
+
+tags:
+  - size
+  - evil
diff --git a/databases/catdat/data/category-properties/locally strongly finitely presentable.yaml b/databases/catdat/data/category-properties/locally strongly finitely presentable.yaml
index e5afddbe9..88c14dc43 100644
--- a/databases/catdat/data/category-properties/locally strongly finitely presentable.yaml	
+++ b/databases/catdat/data/category-properties/locally strongly finitely presentable.yaml	
@@ -18,3 +18,7 @@ related_properties:
   - generalized variety
   - locally finitely presentable
   - multi-algebraic
+
+tags:
+  - algebraicity
+  - accessibility
diff --git a/databases/catdat/data/category-properties/mono-regular.yaml b/databases/catdat/data/category-properties/mono-regular.yaml
index 3602d4b6b..97617a37a 100644
--- a/databases/catdat/data/category-properties/mono-regular.yaml
+++ b/databases/catdat/data/category-properties/mono-regular.yaml
@@ -9,3 +9,6 @@ related_properties:
   - effective congruences
   - normal
   - subobject-trivial
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/multi-algebraic.yaml b/databases/catdat/data/category-properties/multi-algebraic.yaml
index c6564aeda..a63ca0d90 100644
--- a/databases/catdat/data/category-properties/multi-algebraic.yaml
+++ b/databases/catdat/data/category-properties/multi-algebraic.yaml
@@ -19,3 +19,6 @@ related_properties:
   - locally strongly finitely presentable
   - multi-cocomplete
   - sifted colimits
+
+tags:
+  - algebraicity
diff --git a/databases/catdat/data/category-properties/multi-cocomplete.yaml b/databases/catdat/data/category-properties/multi-cocomplete.yaml
index 465bf1e52..c657a3927 100644
--- a/databases/catdat/data/category-properties/multi-cocomplete.yaml
+++ b/databases/catdat/data/category-properties/multi-cocomplete.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - cocomplete
   - multi-initial object
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/multi-complete.yaml b/databases/catdat/data/category-properties/multi-complete.yaml
index 9f8497f66..de19c394b 100644
--- a/databases/catdat/data/category-properties/multi-complete.yaml
+++ b/databases/catdat/data/category-properties/multi-complete.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - complete
   - multi-terminal object
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/multi-initial object.yaml b/databases/catdat/data/category-properties/multi-initial object.yaml
index e6e7d93b6..4c83e57a2 100644
--- a/databases/catdat/data/category-properties/multi-initial object.yaml	
+++ b/databases/catdat/data/category-properties/multi-initial object.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - initial object
   - multi-cocomplete
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/multi-terminal object.yaml b/databases/catdat/data/category-properties/multi-terminal object.yaml
index 8f878ebd6..d1e766b7a 100644
--- a/databases/catdat/data/category-properties/multi-terminal object.yaml	
+++ b/databases/catdat/data/category-properties/multi-terminal object.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - multi-complete
   - terminal object
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/natural numbers object.yaml b/databases/catdat/data/category-properties/natural numbers object.yaml
index bf4c4d22e..1e53b9840 100644
--- a/databases/catdat/data/category-properties/natural numbers object.yaml	
+++ b/databases/catdat/data/category-properties/natural numbers object.yaml	
@@ -12,3 +12,6 @@ invariant_under_equivalences: true
 related_properties:
   - elementary topos
   - finite products
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/normal.yaml b/databases/catdat/data/category-properties/normal.yaml
index 0d9982444..b1af40c1b 100644
--- a/databases/catdat/data/category-properties/normal.yaml
+++ b/databases/catdat/data/category-properties/normal.yaml
@@ -10,3 +10,6 @@ related_properties:
   - kernels
   - mono-regular
   - zero morphisms
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/one-way.yaml b/databases/catdat/data/category-properties/one-way.yaml
index 8a79d1490..e79bb61a7 100644
--- a/databases/catdat/data/category-properties/one-way.yaml
+++ b/databases/catdat/data/category-properties/one-way.yaml
@@ -9,3 +9,6 @@ related_properties:
   - core-thin
   - direct
   - inverse
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/pointed.yaml b/databases/catdat/data/category-properties/pointed.yaml
index 8063da3e3..4d5694d64 100644
--- a/databases/catdat/data/category-properties/pointed.yaml
+++ b/databases/catdat/data/category-properties/pointed.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - initial object
   - terminal object
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/powers.yaml b/databases/catdat/data/category-properties/powers.yaml
index 421153b42..07ceed370 100644
--- a/databases/catdat/data/category-properties/powers.yaml
+++ b/databases/catdat/data/category-properties/powers.yaml
@@ -9,3 +9,6 @@ related_properties:
   - countable powers
   - finite powers
   - products
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/preadditive.yaml b/databases/catdat/data/category-properties/preadditive.yaml
index f14f90729..e620aa8af 100644
--- a/databases/catdat/data/category-properties/preadditive.yaml
+++ b/databases/catdat/data/category-properties/preadditive.yaml
@@ -9,3 +9,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - additive
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/pretopos.yaml b/databases/catdat/data/category-properties/pretopos.yaml
index fd1c19e2a..35eeef154 100644
--- a/databases/catdat/data/category-properties/pretopos.yaml
+++ b/databases/catdat/data/category-properties/pretopos.yaml
@@ -9,3 +9,7 @@ related_properties:
   - extensive
   - elementary topos
   - mono-regular
+
+tags:
+  - topos theory
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/products.yaml b/databases/catdat/data/category-properties/products.yaml
index 71ac979ee..902767009 100644
--- a/databases/catdat/data/category-properties/products.yaml
+++ b/databases/catdat/data/category-properties/products.yaml
@@ -9,3 +9,6 @@ related_properties:
   - complete
   - finite products
   - powers
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/pullbacks.yaml b/databases/catdat/data/category-properties/pullbacks.yaml
index 05b5bbdf3..9ce1f0abb 100644
--- a/databases/catdat/data/category-properties/pullbacks.yaml
+++ b/databases/catdat/data/category-properties/pullbacks.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - binary products
   - wide pullbacks
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/pushouts.yaml b/databases/catdat/data/category-properties/pushouts.yaml
index 60a55438d..38e5b4d81 100644
--- a/databases/catdat/data/category-properties/pushouts.yaml
+++ b/databases/catdat/data/category-properties/pushouts.yaml
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - binary coproducts
   - wide pushouts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/quotient object classifier.yaml b/databases/catdat/data/category-properties/quotient object classifier.yaml
index cbf3c0cc8..e92b1f113 100644
--- a/databases/catdat/data/category-properties/quotient object classifier.yaml	
+++ b/databases/catdat/data/category-properties/quotient object classifier.yaml	
@@ -11,3 +11,6 @@ invariant_under_equivalences: true
 related_properties:
   - finitely cocomplete
   - regular quotient object classifier
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/quotient-trivial.yaml b/databases/catdat/data/category-properties/quotient-trivial.yaml
index 67d64811c..c608b1550 100644
--- a/databases/catdat/data/category-properties/quotient-trivial.yaml
+++ b/databases/catdat/data/category-properties/quotient-trivial.yaml
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 related_properties:
   - epi-regular
   - groupoid
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/quotients of congruences.yaml b/databases/catdat/data/category-properties/quotients of congruences.yaml
index 5308a5d86..4937d2a7c 100644
--- a/databases/catdat/data/category-properties/quotients of congruences.yaml	
+++ b/databases/catdat/data/category-properties/quotients of congruences.yaml	
@@ -11,3 +11,7 @@ related_properties:
   - effective congruences
   - regular
   - Barr-exact
+
+tags:
+  - colimits
+  - congruences
diff --git a/databases/catdat/data/category-properties/reflexive coequalizers.yaml b/databases/catdat/data/category-properties/reflexive coequalizers.yaml
index b8aee6720..314bb14af 100644
--- a/databases/catdat/data/category-properties/reflexive coequalizers.yaml	
+++ b/databases/catdat/data/category-properties/reflexive coequalizers.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - coequalizers
   - sifted colimits
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/regular quotient object classifier.yaml b/databases/catdat/data/category-properties/regular quotient object classifier.yaml
index 291005129..31279cc24 100644
--- a/databases/catdat/data/category-properties/regular quotient object classifier.yaml	
+++ b/databases/catdat/data/category-properties/regular quotient object classifier.yaml	
@@ -11,3 +11,6 @@ invariant_under_equivalences: true
 related_properties:
   - finitely cocomplete
   - quotient object classifier
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/regular subobject classifier.yaml b/databases/catdat/data/category-properties/regular subobject classifier.yaml
index fda2e9017..e361a8189 100644
--- a/databases/catdat/data/category-properties/regular subobject classifier.yaml	
+++ b/databases/catdat/data/category-properties/regular subobject classifier.yaml	
@@ -12,3 +12,6 @@ invariant_under_equivalences: true
 related_properties:
   - finitely complete
   - subobject classifier
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/regular.yaml b/databases/catdat/data/category-properties/regular.yaml
index ba26f0454..b5627c52f 100644
--- a/databases/catdat/data/category-properties/regular.yaml
+++ b/databases/catdat/data/category-properties/regular.yaml
@@ -9,3 +9,6 @@ related_properties:
   - finitely complete
   - quotients of congruences
   - Barr-exact
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/right cancellative.yaml b/databases/catdat/data/category-properties/right cancellative.yaml
index 72b4046f4..2bcdebb22 100644
--- a/databases/catdat/data/category-properties/right cancellative.yaml	
+++ b/databases/catdat/data/category-properties/right cancellative.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - groupoid
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/self-dual.yaml b/databases/catdat/data/category-properties/self-dual.yaml
index bd4d772c6..d6f9e8c4c 100644
--- a/databases/catdat/data/category-properties/self-dual.yaml
+++ b/databases/catdat/data/category-properties/self-dual.yaml
@@ -6,3 +6,6 @@ dual_property: self-dual
 invariant_under_equivalences: true
 
 related_properties: []
+
+tags:
+  - misc
diff --git a/databases/catdat/data/category-properties/semi-strongly connected.yaml b/databases/catdat/data/category-properties/semi-strongly connected.yaml
index 4f1fb35d9..5c6c2bce1 100644
--- a/databases/catdat/data/category-properties/semi-strongly connected.yaml	
+++ b/databases/catdat/data/category-properties/semi-strongly connected.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - connected
   - inhabited
   - strongly connected
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/sequential colimits.yaml b/databases/catdat/data/category-properties/sequential colimits.yaml
index 20db002ac..18ceac5c8 100644
--- a/databases/catdat/data/category-properties/sequential colimits.yaml	
+++ b/databases/catdat/data/category-properties/sequential colimits.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - directed colimits
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/sequential limits.yaml b/databases/catdat/data/category-properties/sequential limits.yaml
index 6ecb32ff2..ad0e627fa 100644
--- a/databases/catdat/data/category-properties/sequential limits.yaml	
+++ b/databases/catdat/data/category-properties/sequential limits.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - directed limits
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/sifted colimits.yaml b/databases/catdat/data/category-properties/sifted colimits.yaml
index acf997099..0a3291257 100644
--- a/databases/catdat/data/category-properties/sifted colimits.yaml	
+++ b/databases/catdat/data/category-properties/sifted colimits.yaml	
@@ -10,3 +10,6 @@ related_properties:
   - filtered colimits
   - reflexive coequalizers
   - sifted
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/sifted.yaml b/databases/catdat/data/category-properties/sifted.yaml
index d9da64307..bd1a351e8 100644
--- a/databases/catdat/data/category-properties/sifted.yaml
+++ b/databases/catdat/data/category-properties/sifted.yaml
@@ -12,3 +12,6 @@ related_properties:
   - connected
   - filtered
   - sifted colimits
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/skeletal.yaml b/databases/catdat/data/category-properties/skeletal.yaml
index 0ba738303..e94747d6f 100644
--- a/databases/catdat/data/category-properties/skeletal.yaml
+++ b/databases/catdat/data/category-properties/skeletal.yaml
@@ -7,3 +7,7 @@ invariant_under_equivalences: false
 
 related_properties:
   - gaunt
+
+tags:
+  - misc
+  - evil
diff --git a/databases/catdat/data/category-properties/small.yaml b/databases/catdat/data/category-properties/small.yaml
index 866b44a3e..cf2bfbfce 100644
--- a/databases/catdat/data/category-properties/small.yaml
+++ b/databases/catdat/data/category-properties/small.yaml
@@ -8,3 +8,7 @@ invariant_under_equivalences: false
 related_properties:
   - essentially small
   - locally small
+
+tags:
+  - size
+  - evil
diff --git a/databases/catdat/data/category-properties/split abelian.yaml b/databases/catdat/data/category-properties/split abelian.yaml
index 91bc46640..a6e00abd1 100644
--- a/databases/catdat/data/category-properties/split abelian.yaml	
+++ b/databases/catdat/data/category-properties/split abelian.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - abelian
+
+tags:
+  - abelian
diff --git a/databases/catdat/data/category-properties/strict initial object.yaml b/databases/catdat/data/category-properties/strict initial object.yaml
index 96e50c35a..40f827385 100644
--- a/databases/catdat/data/category-properties/strict initial object.yaml	
+++ b/databases/catdat/data/category-properties/strict initial object.yaml	
@@ -7,3 +7,7 @@ invariant_under_equivalences: true
 
 related_properties:
   - initial object
+
+tags:
+  - colimits
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/strict terminal object.yaml b/databases/catdat/data/category-properties/strict terminal object.yaml
index cb72965b3..542f5f335 100644
--- a/databases/catdat/data/category-properties/strict terminal object.yaml	
+++ b/databases/catdat/data/category-properties/strict terminal object.yaml	
@@ -7,3 +7,7 @@ invariant_under_equivalences: true
 
 related_properties:
   - terminal object
+
+tags:
+  - limits
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/strongly connected.yaml b/databases/catdat/data/category-properties/strongly connected.yaml
index aad8550d8..a41bcc8b0 100644
--- a/databases/catdat/data/category-properties/strongly connected.yaml	
+++ b/databases/catdat/data/category-properties/strongly connected.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - connected
   - inhabited
   - semi-strongly connected
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/subobject classifier.yaml b/databases/catdat/data/category-properties/subobject classifier.yaml
index d19b772a1..54c081529 100644
--- a/databases/catdat/data/category-properties/subobject classifier.yaml	
+++ b/databases/catdat/data/category-properties/subobject classifier.yaml	
@@ -13,3 +13,6 @@ related_properties:
   - elementary topos
   - finitely complete
   - regular subobject classifier
+
+tags:
+  - topos theory
diff --git a/databases/catdat/data/category-properties/subobject-trivial.yaml b/databases/catdat/data/category-properties/subobject-trivial.yaml
index 4802d42d8..b4ca07de7 100644
--- a/databases/catdat/data/category-properties/subobject-trivial.yaml
+++ b/databases/catdat/data/category-properties/subobject-trivial.yaml
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 related_properties:
   - groupoid
   - mono-regular
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/terminal object.yaml b/databases/catdat/data/category-properties/terminal object.yaml
index 09e95c3e3..d91cf40b7 100644
--- a/databases/catdat/data/category-properties/terminal object.yaml	
+++ b/databases/catdat/data/category-properties/terminal object.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - finite products
   - multi-terminal object
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/thin.yaml b/databases/catdat/data/category-properties/thin.yaml
index dacb9d735..26e4bcd41 100644
--- a/databases/catdat/data/category-properties/thin.yaml
+++ b/databases/catdat/data/category-properties/thin.yaml
@@ -9,3 +9,6 @@ related_properties:
   - core-thin
   - discrete
   - locally finite
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/category-properties/trivial.yaml b/databases/catdat/data/category-properties/trivial.yaml
index 188dba469..8a929e50a 100644
--- a/databases/catdat/data/category-properties/trivial.yaml
+++ b/databases/catdat/data/category-properties/trivial.yaml
@@ -6,3 +6,6 @@ dual_property: trivial
 invariant_under_equivalences: true
 
 related_properties: []
+
+tags:
+  - misc
diff --git a/databases/catdat/data/category-properties/unital.yaml b/databases/catdat/data/category-properties/unital.yaml
index 43d75ea5c..be1d1ef56 100644
--- a/databases/catdat/data/category-properties/unital.yaml
+++ b/databases/catdat/data/category-properties/unital.yaml
@@ -9,3 +9,6 @@ related_properties:
   - Malcev
   - finitely complete
   - pointed
+
+tags:
+  - limit–colimit interaction
diff --git a/databases/catdat/data/category-properties/well-copowered.yaml b/databases/catdat/data/category-properties/well-copowered.yaml
index 03065a855..b25258106 100644
--- a/databases/catdat/data/category-properties/well-copowered.yaml
+++ b/databases/catdat/data/category-properties/well-copowered.yaml
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - small
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/well-powered.yaml b/databases/catdat/data/category-properties/well-powered.yaml
index c7353d62e..cd9880668 100644
--- a/databases/catdat/data/category-properties/well-powered.yaml
+++ b/databases/catdat/data/category-properties/well-powered.yaml
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - small
+
+tags:
+  - size
diff --git a/databases/catdat/data/category-properties/wide pullbacks.yaml b/databases/catdat/data/category-properties/wide pullbacks.yaml
index a4312308c..226b9de6c 100644
--- a/databases/catdat/data/category-properties/wide pullbacks.yaml	
+++ b/databases/catdat/data/category-properties/wide pullbacks.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - pullbacks
+
+tags:
+  - limits
diff --git a/databases/catdat/data/category-properties/wide pushouts.yaml b/databases/catdat/data/category-properties/wide pushouts.yaml
index ce2b274a9..0c71d2c57 100644
--- a/databases/catdat/data/category-properties/wide pushouts.yaml	
+++ b/databases/catdat/data/category-properties/wide pushouts.yaml	
@@ -7,3 +7,6 @@ invariant_under_equivalences: true
 
 related_properties:
   - pushouts
+
+tags:
+  - colimits
diff --git a/databases/catdat/data/category-properties/zero morphisms.yaml b/databases/catdat/data/category-properties/zero morphisms.yaml
index 34f26ea29..05e8e2aa5 100644
--- a/databases/catdat/data/category-properties/zero morphisms.yaml	
+++ b/databases/catdat/data/category-properties/zero morphisms.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 related_properties:
   - pointed
   - preadditive
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/config.yaml b/databases/catdat/data/config.yaml
index cf810c3a0..20ede6d85 100644
--- a/databases/catdat/data/config.yaml
+++ b/databases/catdat/data/config.yaml
@@ -18,7 +18,19 @@ functor_tags:
   - forgetful
   - free
 
-category_property_tags: []
+category_property_tags:
+  - limits
+  - colimits
+  - limit–colimit interaction
+  - morphism behavior
+  - size
+  - algebraicity
+  - accessibility
+  - topos theory
+  - abelian
+  - congruences
+  - misc
+  - evil
 
 functor_property_tags: []
 
diff --git a/src/pages/PropertyPage.svelte b/src/pages/PropertyPage.svelte
index 8dc08df34..e8109f2d1 100644
--- a/src/pages/PropertyPage.svelte
+++ b/src/pages/PropertyPage.svelte
@@ -55,7 +55,10 @@
 	{@html property.description}
 
 	{#if property.invariant_under_equivalences === false}
-		Warning: This property is not invariant under equivalences.
+		Warning: This property is not <a
+			href="https://ncatlab.org/nlab/show/principle+of+equivalence"
+			target="_blank">invariant under equivalences</a
+		>.
 	{/if}
 </p>
 

From c57159d539f3162aee2bdfab668776102122a832 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 09:21:31 +0200
Subject: [PATCH 5/9] add tags to all properties of functors

---
 .cspell.json                                             | 1 +
 databases/catdat/data/config.yaml                        | 9 ++++++++-
 .../catdat/data/functor-properties/cocontinuous.yaml     | 3 +++
 databases/catdat/data/functor-properties/cofinitary.yaml | 3 +++
 databases/catdat/data/functor-properties/comonadic.yaml  | 3 +++
 .../catdat/data/functor-properties/conservative.yaml     | 5 ++++-
 databases/catdat/data/functor-properties/continuous.yaml | 3 +++
 .../catdat/data/functor-properties/coreflector.yaml      | 3 +++
 databases/catdat/data/functor-properties/dominant.yaml   | 3 +++
 .../catdat/data/functor-properties/equivalence.yaml      | 3 +++
 .../data/functor-properties/essentially injective.yaml   | 3 +++
 .../data/functor-properties/essentially surjective.yaml  | 3 +++
 databases/catdat/data/functor-properties/exact.yaml      | 4 ++++
 databases/catdat/data/functor-properties/faithful.yaml   | 3 +++
 databases/catdat/data/functor-properties/finitary.yaml   | 3 +++
 .../data/functor-properties/full-on-isomorphisms.yaml    | 3 +++
 databases/catdat/data/functor-properties/full.yaml       | 3 +++
 .../catdat/data/functor-properties/fully faithful.yaml   | 3 +++
 .../catdat/data/functor-properties/left adjoint.yaml     | 3 +++
 databases/catdat/data/functor-properties/left exact.yaml | 3 +++
 .../catdat/data/functor-properties/left-invertible.yaml  | 3 +++
 databases/catdat/data/functor-properties/monadic.yaml    | 3 +++
 .../functor-properties/preserves binary coproducts.yaml  | 3 +++
 .../functor-properties/preserves binary products.yaml    | 3 +++
 .../data/functor-properties/preserves coequalizers.yaml  | 3 +++
 .../data/functor-properties/preserves coproducts.yaml    | 3 +++
 .../preserves coreflexive equalizers.yaml                | 3 +++
 .../data/functor-properties/preserves epimorphisms.yaml  | 3 +++
 .../data/functor-properties/preserves equalizers.yaml    | 3 +++
 .../functor-properties/preserves finite coproducts.yaml  | 3 +++
 .../functor-properties/preserves finite products.yaml    | 3 +++
 .../functor-properties/preserves initial objects.yaml    | 4 ++++
 .../data/functor-properties/preserves monomorphisms.yaml | 3 +++
 .../data/functor-properties/preserves products.yaml      | 3 +++
 .../preserves reflexive coequalizers.yaml                | 3 +++
 .../functor-properties/preserves terminal objects.yaml   | 4 ++++
 .../catdat/data/functor-properties/pseudomonic.yaml      | 3 +++
 databases/catdat/data/functor-properties/reflector.yaml  | 3 +++
 .../catdat/data/functor-properties/representable.yaml    | 3 +++
 .../catdat/data/functor-properties/right adjoint.yaml    | 3 +++
 .../catdat/data/functor-properties/right exact.yaml      | 3 +++
 .../catdat/data/functor-properties/right-invertible.yaml | 3 +++
 42 files changed, 133 insertions(+), 2 deletions(-)

diff --git a/.cspell.json b/.cspell.json
index ba45cc2ce..051387da2 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -177,6 +177,7 @@
 		"injections",
 		"injective",
 		"injectivity",
+		"invertibility",
 		"Isbell",
 		"Johnstone",
 		"Jónsson",
diff --git a/databases/catdat/data/config.yaml b/databases/catdat/data/config.yaml
index 20ede6d85..1c596e0cc 100644
--- a/databases/catdat/data/config.yaml
+++ b/databases/catdat/data/config.yaml
@@ -32,7 +32,14 @@ category_property_tags:
   - misc
   - evil
 
-functor_property_tags: []
+functor_property_tags:
+  - limit preservation
+  - colimit preservation
+  - morphism behavior
+  - object behavior
+  - adjunctions
+  - invertibility
+  - misc
 
 relations:
   - relation: is
diff --git a/databases/catdat/data/functor-properties/cocontinuous.yaml b/databases/catdat/data/functor-properties/cocontinuous.yaml
index 54ea6f3e3..e381e3666 100644
--- a/databases/catdat/data/functor-properties/cocontinuous.yaml
+++ b/databases/catdat/data/functor-properties/cocontinuous.yaml
@@ -10,3 +10,6 @@ related_properties:
   - left adjoint
   - preserves coequalizers
   - finitary
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/cofinitary.yaml b/databases/catdat/data/functor-properties/cofinitary.yaml
index c707d5e0c..effc3c08d 100644
--- a/databases/catdat/data/functor-properties/cofinitary.yaml
+++ b/databases/catdat/data/functor-properties/cofinitary.yaml
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 dual_property: finitary
 related_properties:
   - continuous
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/comonadic.yaml b/databases/catdat/data/functor-properties/comonadic.yaml
index 157f47790..8d3d8c863 100644
--- a/databases/catdat/data/functor-properties/comonadic.yaml
+++ b/databases/catdat/data/functor-properties/comonadic.yaml
@@ -7,3 +7,6 @@ dual_property: monadic
 related_properties:
   - left adjoint
   - faithful
+
+tags:
+  - adjunctions
diff --git a/databases/catdat/data/functor-properties/conservative.yaml b/databases/catdat/data/functor-properties/conservative.yaml
index f171a3661..af48f4471 100644
--- a/databases/catdat/data/functor-properties/conservative.yaml
+++ b/databases/catdat/data/functor-properties/conservative.yaml
@@ -1,6 +1,6 @@
 id: conservative
 relation: is
-description: 'A functor $F : \C \to \D$ is <i>conservative</i> when it is isomorphic-reflecting: If $f$ is a morphism in $\C$ such that $F(f)$ is an isomorphism, then $f$ is an isomorphism.'
+description: 'A functor $F : \C \to \D$ is <i>conservative</i> when it is isomorphism-reflecting: If $f$ is a morphism in $\C$ such that $F(f)$ is an isomorphism, then $f$ is an isomorphism.'
 nlab_link: https://ncatlab.org/nlab/show/conservative+functor
 invariant_under_equivalences: true
 dual_property: conservative
@@ -8,3 +8,6 @@ related_properties:
   - fully faithful
   - essentially injective
   - full on isomorphisms
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/continuous.yaml b/databases/catdat/data/functor-properties/continuous.yaml
index 4739d6cfa..fa7af4451 100644
--- a/databases/catdat/data/functor-properties/continuous.yaml
+++ b/databases/catdat/data/functor-properties/continuous.yaml
@@ -10,3 +10,6 @@ related_properties:
   - right adjoint
   - preserves equalizers
   - cofinitary
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/coreflector.yaml b/databases/catdat/data/functor-properties/coreflector.yaml
index d0f7659e8..240dc0b9d 100644
--- a/databases/catdat/data/functor-properties/coreflector.yaml
+++ b/databases/catdat/data/functor-properties/coreflector.yaml
@@ -7,3 +7,6 @@ dual_property: reflector
 related_properties:
   - right adjoint
   - right-invertible
+
+tags:
+  - adjunctions
diff --git a/databases/catdat/data/functor-properties/dominant.yaml b/databases/catdat/data/functor-properties/dominant.yaml
index 87ab918b0..e41dc0d6e 100644
--- a/databases/catdat/data/functor-properties/dominant.yaml
+++ b/databases/catdat/data/functor-properties/dominant.yaml
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 dual_property: dominant
 related_properties:
   - essentially surjective
+
+tags:
+  - object behavior
diff --git a/databases/catdat/data/functor-properties/equivalence.yaml b/databases/catdat/data/functor-properties/equivalence.yaml
index 4d3f4d2b2..ea2f45649 100644
--- a/databases/catdat/data/functor-properties/equivalence.yaml
+++ b/databases/catdat/data/functor-properties/equivalence.yaml
@@ -11,3 +11,6 @@ related_properties:
   - continuous
   - cocontinuous
   - left-invertible
+
+tags:
+  - invertibility
diff --git a/databases/catdat/data/functor-properties/essentially injective.yaml b/databases/catdat/data/functor-properties/essentially injective.yaml
index 72075ef09..39a934878 100644
--- a/databases/catdat/data/functor-properties/essentially injective.yaml	
+++ b/databases/catdat/data/functor-properties/essentially injective.yaml	
@@ -13,3 +13,6 @@ related_properties:
   - full on isomorphisms
   - essentially surjective
   - pseudomonic
+
+tags:
+  - object behavior
diff --git a/databases/catdat/data/functor-properties/essentially surjective.yaml b/databases/catdat/data/functor-properties/essentially surjective.yaml
index 60c29bb35..1e8f32f7b 100644
--- a/databases/catdat/data/functor-properties/essentially surjective.yaml	
+++ b/databases/catdat/data/functor-properties/essentially surjective.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - equivalence
   - essentially injective
   - dominant
+
+tags:
+  - object behavior
diff --git a/databases/catdat/data/functor-properties/exact.yaml b/databases/catdat/data/functor-properties/exact.yaml
index bf21e571c..1c0336848 100644
--- a/databases/catdat/data/functor-properties/exact.yaml
+++ b/databases/catdat/data/functor-properties/exact.yaml
@@ -9,3 +9,7 @@ related_properties:
   - right exact
   - continuous
   - cocontinuous
+
+tags:
+  - limit preservation
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/faithful.yaml b/databases/catdat/data/functor-properties/faithful.yaml
index 4054ca910..cf06019f5 100644
--- a/databases/catdat/data/functor-properties/faithful.yaml
+++ b/databases/catdat/data/functor-properties/faithful.yaml
@@ -10,3 +10,6 @@ related_properties:
   - essentially injective
   - left-invertible
   - pseudomonic
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/finitary.yaml b/databases/catdat/data/functor-properties/finitary.yaml
index 5aa51b476..1f44c1c74 100644
--- a/databases/catdat/data/functor-properties/finitary.yaml
+++ b/databases/catdat/data/functor-properties/finitary.yaml
@@ -6,3 +6,6 @@ invariant_under_equivalences: true
 dual_property: cofinitary
 related_properties:
   - cocontinuous
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/full-on-isomorphisms.yaml b/databases/catdat/data/functor-properties/full-on-isomorphisms.yaml
index 112e50c4a..812223bc6 100644
--- a/databases/catdat/data/functor-properties/full-on-isomorphisms.yaml
+++ b/databases/catdat/data/functor-properties/full-on-isomorphisms.yaml
@@ -8,3 +8,6 @@ related_properties:
   - full
   - conservative
   - essentially injective
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/full.yaml b/databases/catdat/data/functor-properties/full.yaml
index b01e8024e..f18d29d5a 100644
--- a/databases/catdat/data/functor-properties/full.yaml
+++ b/databases/catdat/data/functor-properties/full.yaml
@@ -10,3 +10,6 @@ related_properties:
   - fully faithful
   - essentially injective
   - full on isomorphisms
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/fully faithful.yaml b/databases/catdat/data/functor-properties/fully faithful.yaml
index 996e82b18..4e23f94fa 100644
--- a/databases/catdat/data/functor-properties/fully faithful.yaml	
+++ b/databases/catdat/data/functor-properties/fully faithful.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - faithful
   - equivalence
   - pseudomonic
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/left adjoint.yaml b/databases/catdat/data/functor-properties/left adjoint.yaml
index c2675966a..70b932705 100644
--- a/databases/catdat/data/functor-properties/left adjoint.yaml	
+++ b/databases/catdat/data/functor-properties/left adjoint.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - cocontinuous
   - comonadic
   - reflector
+
+tags:
+  - adjunctions
diff --git a/databases/catdat/data/functor-properties/left exact.yaml b/databases/catdat/data/functor-properties/left exact.yaml
index 093a9eb3e..5f662499b 100644
--- a/databases/catdat/data/functor-properties/left exact.yaml	
+++ b/databases/catdat/data/functor-properties/left exact.yaml	
@@ -7,3 +7,6 @@ dual_property: right exact
 related_properties:
   - exact
   - continuous
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/left-invertible.yaml b/databases/catdat/data/functor-properties/left-invertible.yaml
index 95fa1ddb4..5b789463d 100644
--- a/databases/catdat/data/functor-properties/left-invertible.yaml
+++ b/databases/catdat/data/functor-properties/left-invertible.yaml
@@ -9,3 +9,6 @@ related_properties:
   - faithful
   - essentially injective
   - right-invertible
+
+tags:
+  - invertibility
diff --git a/databases/catdat/data/functor-properties/monadic.yaml b/databases/catdat/data/functor-properties/monadic.yaml
index f28acda1e..320ae4e59 100644
--- a/databases/catdat/data/functor-properties/monadic.yaml
+++ b/databases/catdat/data/functor-properties/monadic.yaml
@@ -7,3 +7,6 @@ dual_property: comonadic
 related_properties:
   - right adjoint
   - faithful
+
+tags:
+  - adjunctions
diff --git a/databases/catdat/data/functor-properties/preserves binary coproducts.yaml b/databases/catdat/data/functor-properties/preserves binary coproducts.yaml
index 83d83b460..66406454d 100644
--- a/databases/catdat/data/functor-properties/preserves binary coproducts.yaml	
+++ b/databases/catdat/data/functor-properties/preserves binary coproducts.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - preserves finite products
   - preserves products
   - continuous
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/preserves binary products.yaml b/databases/catdat/data/functor-properties/preserves binary products.yaml
index b3f870871..fa3587e54 100644
--- a/databases/catdat/data/functor-properties/preserves binary products.yaml	
+++ b/databases/catdat/data/functor-properties/preserves binary products.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - preserves finite products
   - preserves products
   - continuous
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/preserves coequalizers.yaml b/databases/catdat/data/functor-properties/preserves coequalizers.yaml
index 284a17128..2ee51ee8f 100644
--- a/databases/catdat/data/functor-properties/preserves coequalizers.yaml	
+++ b/databases/catdat/data/functor-properties/preserves coequalizers.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - cocontinuous
   - right exact
   - preserves reflexive coequalizers
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/preserves coproducts.yaml b/databases/catdat/data/functor-properties/preserves coproducts.yaml
index e66fb010a..f8af6d5cf 100644
--- a/databases/catdat/data/functor-properties/preserves coproducts.yaml	
+++ b/databases/catdat/data/functor-properties/preserves coproducts.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - preserves finite coproducts
   - preserves initial objects
   - cocontinuous
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/preserves coreflexive equalizers.yaml b/databases/catdat/data/functor-properties/preserves coreflexive equalizers.yaml
index dc916cf63..aa81f6b0b 100644
--- a/databases/catdat/data/functor-properties/preserves coreflexive equalizers.yaml	
+++ b/databases/catdat/data/functor-properties/preserves coreflexive equalizers.yaml	
@@ -7,3 +7,6 @@ dual_property: preserves reflexive coequalizers
 related_properties:
   - continuous
   - preserves equalizers
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/preserves epimorphisms.yaml b/databases/catdat/data/functor-properties/preserves epimorphisms.yaml
index ae15a5812..ae8cc4535 100644
--- a/databases/catdat/data/functor-properties/preserves epimorphisms.yaml	
+++ b/databases/catdat/data/functor-properties/preserves epimorphisms.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 dual_property: preserves monomorphisms
 related_properties:
   - right exact
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/preserves equalizers.yaml b/databases/catdat/data/functor-properties/preserves equalizers.yaml
index be7bd0659..86bc9420b 100644
--- a/databases/catdat/data/functor-properties/preserves equalizers.yaml	
+++ b/databases/catdat/data/functor-properties/preserves equalizers.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - continuous
   - left exact
   - preserves coreflexive equalizers
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/preserves finite coproducts.yaml b/databases/catdat/data/functor-properties/preserves finite coproducts.yaml
index 8a44ad138..0b4a3f436 100644
--- a/databases/catdat/data/functor-properties/preserves finite coproducts.yaml	
+++ b/databases/catdat/data/functor-properties/preserves finite coproducts.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - preserves binary coproducts
   - preserves initial objects
   - cocontinuous
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/preserves finite products.yaml b/databases/catdat/data/functor-properties/preserves finite products.yaml
index 2f752ae62..c50daebc3 100644
--- a/databases/catdat/data/functor-properties/preserves finite products.yaml	
+++ b/databases/catdat/data/functor-properties/preserves finite products.yaml	
@@ -9,3 +9,6 @@ related_properties:
   - preserves binary products
   - preserves terminal objects
   - continuous
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/preserves initial objects.yaml b/databases/catdat/data/functor-properties/preserves initial objects.yaml
index ee5466f51..710522c06 100644
--- a/databases/catdat/data/functor-properties/preserves initial objects.yaml	
+++ b/databases/catdat/data/functor-properties/preserves initial objects.yaml	
@@ -7,3 +7,7 @@ dual_property: preserves terminal objects
 related_properties:
   - preserves finite coproducts
   - cocontinuous
+
+tags:
+  - colimit preservation
+  - object behavior
diff --git a/databases/catdat/data/functor-properties/preserves monomorphisms.yaml b/databases/catdat/data/functor-properties/preserves monomorphisms.yaml
index 8dee80c98..177ead440 100644
--- a/databases/catdat/data/functor-properties/preserves monomorphisms.yaml	
+++ b/databases/catdat/data/functor-properties/preserves monomorphisms.yaml	
@@ -8,3 +8,6 @@ invariant_under_equivalences: true
 dual_property: preserves epimorphisms
 related_properties:
   - left exact
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/preserves products.yaml b/databases/catdat/data/functor-properties/preserves products.yaml
index 339b73caa..d0472a0e6 100644
--- a/databases/catdat/data/functor-properties/preserves products.yaml	
+++ b/databases/catdat/data/functor-properties/preserves products.yaml	
@@ -8,3 +8,6 @@ related_properties:
   - preserves finite products
   - preserves terminal objects
   - continuous
+
+tags:
+  - limit preservation
diff --git a/databases/catdat/data/functor-properties/preserves reflexive coequalizers.yaml b/databases/catdat/data/functor-properties/preserves reflexive coequalizers.yaml
index c33b1c5b7..af37aeccd 100644
--- a/databases/catdat/data/functor-properties/preserves reflexive coequalizers.yaml	
+++ b/databases/catdat/data/functor-properties/preserves reflexive coequalizers.yaml	
@@ -7,3 +7,6 @@ dual_property: preserves coreflexive equalizers
 related_properties:
   - cocontinuous
   - preserves coequalizers
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/preserves terminal objects.yaml b/databases/catdat/data/functor-properties/preserves terminal objects.yaml
index 3ef7fc350..12c1a989c 100644
--- a/databases/catdat/data/functor-properties/preserves terminal objects.yaml	
+++ b/databases/catdat/data/functor-properties/preserves terminal objects.yaml	
@@ -7,3 +7,7 @@ dual_property: preserves initial objects
 related_properties:
   - preserves finite products
   - continuous
+
+tags:
+  - limit preservation
+  - object behavior
diff --git a/databases/catdat/data/functor-properties/pseudomonic.yaml b/databases/catdat/data/functor-properties/pseudomonic.yaml
index 538cbc6b4..f97a7efac 100644
--- a/databases/catdat/data/functor-properties/pseudomonic.yaml
+++ b/databases/catdat/data/functor-properties/pseudomonic.yaml
@@ -8,3 +8,6 @@ related_properties:
   - essentially injective
   - full on isomorphisms
   - faithful
+
+tags:
+  - morphism behavior
diff --git a/databases/catdat/data/functor-properties/reflector.yaml b/databases/catdat/data/functor-properties/reflector.yaml
index f631e50af..9a4b459dc 100644
--- a/databases/catdat/data/functor-properties/reflector.yaml
+++ b/databases/catdat/data/functor-properties/reflector.yaml
@@ -7,3 +7,6 @@ dual_property: coreflector
 related_properties:
   - left adjoint
   - right-invertible
+
+tags:
+  - adjunctions
diff --git a/databases/catdat/data/functor-properties/representable.yaml b/databases/catdat/data/functor-properties/representable.yaml
index e5ec76dbe..1ef254802 100644
--- a/databases/catdat/data/functor-properties/representable.yaml
+++ b/databases/catdat/data/functor-properties/representable.yaml
@@ -5,3 +5,6 @@ nlab_link: https://ncatlab.org/nlab/show/representable+functor
 invariant_under_equivalences: true
 related_properties:
   - continuous
+
+tags:
+  - misc
diff --git a/databases/catdat/data/functor-properties/right adjoint.yaml b/databases/catdat/data/functor-properties/right adjoint.yaml
index 8369ac73d..adc15c72f 100644
--- a/databases/catdat/data/functor-properties/right adjoint.yaml	
+++ b/databases/catdat/data/functor-properties/right adjoint.yaml	
@@ -7,3 +7,6 @@ dual_property: left adjoint
 related_properties:
   - continuous
   - monadic
+
+tags:
+  - adjunctions
diff --git a/databases/catdat/data/functor-properties/right exact.yaml b/databases/catdat/data/functor-properties/right exact.yaml
index 9790abd64..37c07196d 100644
--- a/databases/catdat/data/functor-properties/right exact.yaml	
+++ b/databases/catdat/data/functor-properties/right exact.yaml	
@@ -7,3 +7,6 @@ dual_property: left exact
 related_properties:
   - exact
   - cocontinuous
+
+tags:
+  - colimit preservation
diff --git a/databases/catdat/data/functor-properties/right-invertible.yaml b/databases/catdat/data/functor-properties/right-invertible.yaml
index d0883f87b..05a0f6a98 100644
--- a/databases/catdat/data/functor-properties/right-invertible.yaml
+++ b/databases/catdat/data/functor-properties/right-invertible.yaml
@@ -9,3 +9,6 @@ related_properties:
   - essentially surjective
   - left-invertible
   - reflector
+
+tags:
+  - invertibility

From 8d4bbd864817855e58df9ed68b9bb08e30fdc21d Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 12:13:24 +0200
Subject: [PATCH 6/9] activate properties link in nav on tag pages

---
 src/components/Nav.svelte |  2 +-
 src/lib/client/nav.ts     | 12 ++++++------
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/components/Nav.svelte b/src/components/Nav.svelte
index fe97ed93b..77eec1260 100644
--- a/src/components/Nav.svelte
+++ b/src/components/Nav.svelte
@@ -17,7 +17,7 @@
 		{#each get_navigation_links(selected_type) as { nested, href, text, icon }}
 			<li
 				class:current={page.url.pathname === href ||
-					(nested && page.url.pathname.startsWith(nested))}
+					(nested && nested.some((path) => page.url.pathname.startsWith(path)))}
 			>
 				<a {href}><Fa {icon} scale={0.85} /> {text}</a>
 			</li>
diff --git a/src/lib/client/nav.ts b/src/lib/client/nav.ts
index caac1959f..61e52c931 100644
--- a/src/lib/client/nav.ts
+++ b/src/lib/client/nav.ts
@@ -20,7 +20,7 @@ import { PLURALS } from '$lib/commons/structures'
 type Link = {
 	href: string
 	text: string
-	nested?: string
+	nested?: string[]
 	icon: IconDefinition
 }
 
@@ -34,32 +34,32 @@ export function get_navigation_links(type: StructureType): Link[] {
 		{
 			href: `/${PLURALS[type]}`,
 			text: capitalize(PLURALS[type]),
-			nested: `/${type}/`,
+			nested: [`/${type}/`, `/${PLURALS[type]}/`],
 			icon: faDatabase,
 		},
 		{
 			href: `/${type}-properties`,
 			text: `Properties`,
-			nested: `/${type}-property/`,
+			nested: [`/${type}-property/`, `/${type}-properties/`],
 			icon: faList,
 		},
 		{
 			href: `/${type}-implications`,
 			text: `Implications`,
-			nested: `/${type}-implication`,
+			nested: [`/${type}-implication`],
 			icon: faArrowsSplitUpAndLeft,
 		},
 		{
 			href: `/${type}-comparison`,
 			text: `Compare`,
 			icon: faChartBar,
-			nested: `/${type}-comparison`,
+			nested: [`/${type}-comparison`],
 		},
 		{
 			href: `/${type}-search`,
 			text: `Search`,
 			icon: faSearch,
-			nested: `/${type}-search/results`,
+			nested: [`/${type}-search/results`],
 		},
 	]
 }

From 6df3ad37c4425e6279b0a0ea539ae47ae97c91a9 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 12:19:43 +0200
Subject: [PATCH 7/9] simplify headings of tag pages and tag sections

---
 src/pages/PropertyListPage.svelte     | 2 +-
 src/pages/StructureListPage.svelte    | 2 +-
 src/pages/TaggedPropertiesPage.svelte | 5 +++--
 src/pages/TaggedStructuresPage.svelte | 6 +++---
 4 files changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/pages/PropertyListPage.svelte b/src/pages/PropertyListPage.svelte
index f556458af..a19313d5b 100644
--- a/src/pages/PropertyListPage.svelte
+++ b/src/pages/PropertyListPage.svelte
@@ -67,7 +67,7 @@
 
 {#if tags.length > 0}
 	<section class="tag-section">
-		<h2>List of tags</h2>
+		<h2>Tags</h2>
 
 		<TagList {tags} {type} sort="property" />
 	</section>
diff --git a/src/pages/StructureListPage.svelte b/src/pages/StructureListPage.svelte
index cb0759f20..08ba5b0e8 100644
--- a/src/pages/StructureListPage.svelte
+++ b/src/pages/StructureListPage.svelte
@@ -56,7 +56,7 @@
 </section>
 
 <section>
-	<h2>List of tags</h2>
+	<h2>Tags</h2>
 
 	<TagList {tags} {type} sort="structure" />
 </section>
diff --git a/src/pages/TaggedPropertiesPage.svelte b/src/pages/TaggedPropertiesPage.svelte
index be348d809..c8f3e2d6e 100644
--- a/src/pages/TaggedPropertiesPage.svelte
+++ b/src/pages/TaggedPropertiesPage.svelte
@@ -3,6 +3,7 @@
 	import { pluralize } from '$lib/client/utils'
 	import type { PropertyShort, StructureType } from '$lib/commons/types'
 	import PropertyList from '$components/PropertyList.svelte'
+	import { PLURALS } from '$lib/commons/structures'
 
 	type Props = {
 		type: StructureType
@@ -13,9 +14,9 @@
 	let { type, properties, tag }: Props = $props()
 </script>
 
-<MetaData title="List of {type} properties tagged with '{tag}'" />
+<MetaData title="Properties of {PLURALS[type]} tagged with '{tag}'" />
 
-<h2>List of {type} properties tagged with '{tag}'</h2>
+<h2>Properties of {PLURALS[type]} tagged with '{tag}'</h2>
 
 <p class="hint">
 	{pluralize(properties.length, {
diff --git a/src/pages/TaggedStructuresPage.svelte b/src/pages/TaggedStructuresPage.svelte
index 7b7486f26..c496f138c 100644
--- a/src/pages/TaggedStructuresPage.svelte
+++ b/src/pages/TaggedStructuresPage.svelte
@@ -1,7 +1,7 @@
 <script lang="ts">
 	import StructureList from '$components/StructureList.svelte'
 	import MetaData from '$components/MetaData.svelte'
-	import { pluralize } from '$lib/client/utils'
+	import { capitalize, pluralize } from '$lib/client/utils'
 	import type { StructureShort, StructureType } from '$lib/commons/types'
 	import { PLURALS } from '$lib/commons/structures'
 
@@ -14,9 +14,9 @@
 	let { type, structures, tag }: Props = $props()
 </script>
 
-<MetaData title="List of {PLURALS[type]} tagged with '{tag}'" />
+<MetaData title="{capitalize(PLURALS[type])} tagged with '{tag}'" />
 
-<h2>List of {PLURALS[type]} tagged with '{tag}'</h2>
+<h2>{capitalize(PLURALS[type])} tagged with '{tag}'</h2>
 
 <p class="hint">
 	{pluralize(structures.length, {

From 5e521109bf3ba3bde68c812b07149cf0e60fbfb8 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 16:59:28 +0200
Subject: [PATCH 8/9] enforce that each structure and property has at least one
 tag

---
 databases/catdat/scripts/seed.ts             | 13 +++++++++++--
 databases/catdat/scripts/utils/seed.types.ts |  2 +-
 src/pages/PropertyPage.svelte                |  5 +----
 3 files changed, 13 insertions(+), 7 deletions(-)

diff --git a/databases/catdat/scripts/seed.ts b/databases/catdat/scripts/seed.ts
index ffe8ca2be..91abc95c6 100644
--- a/databases/catdat/scripts/seed.ts
+++ b/databases/catdat/scripts/seed.ts
@@ -221,6 +221,11 @@ function seed_structures<T extends StructureYaml>({
 			structure[`dual_${type}`] || null,
 		)
 
+		if (!structure.tags.length) {
+			console.error(`❌ Structure "${structure.id}" has no tags`)
+			process.exit(1)
+		}
+
 		for (const tag of structure.tags) {
 			tag_insert.run(structure.id, tag, type)
 		}
@@ -334,8 +339,12 @@ function seed_properties({ type, folder }: { type: StructureType; folder: string
 			related_insert.run(property.id, related, type)
 		}
 
-		for (const tag of property.tags ?? []) {
-			// TODO: remove ?? when tags are filled
+		if (!property.tags.length) {
+			console.error(`❌ Property "${property.id}" has no tags`)
+			process.exit(1)
+		}
+
+		for (const tag of property.tags) {
 			tag_insert.run(property.id, tag, type)
 		}
 	}
diff --git a/databases/catdat/scripts/utils/seed.types.ts b/databases/catdat/scripts/utils/seed.types.ts
index 932569e15..2d0b24d04 100644
--- a/databases/catdat/scripts/utils/seed.types.ts
+++ b/databases/catdat/scripts/utils/seed.types.ts
@@ -73,7 +73,7 @@ export type PropertyYaml = {
 	dual_property?: string | null
 	invariant_under_equivalences: boolean
 	related_properties: string[]
-	tags?: string[]
+	tags: string[]
 }
 
 export type ImplicationYaml = {
diff --git a/src/pages/PropertyPage.svelte b/src/pages/PropertyPage.svelte
index e8109f2d1..97728efe5 100644
--- a/src/pages/PropertyPage.svelte
+++ b/src/pages/PropertyPage.svelte
@@ -46,10 +46,7 @@
 
 <h2>{property.id}</h2>
 
-{#if tags.length}
-	<!-- TODO: remove this if-check later -->
-	<TagList {tags} {type} sort="property" />
-{/if}
+<TagList {tags} {type} sort="property" />
 
 <p>
 	{@html property.description}

From 5ac252b5d048295502f7553caba14d6e5eced717 Mon Sep 17 00:00:00 2001
From: Script Raccoon <scriptraccoon@gmail.com>
Date: Wed, 1 Jul 2026 17:08:02 +0200
Subject: [PATCH 9/9] update database diagram

---
 DATABASE.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/DATABASE.md b/DATABASE.md
index 6c54383f5..7f237d89c 100644
--- a/DATABASE.md
+++ b/DATABASE.md
@@ -108,9 +108,9 @@ to check for redundant assignments of properties to categorical structures.
 
 ## Diagram
 
-This is the database schema as of 17.06.2026; changes may occur.
+This is the database schema as of 01.07.2026; changes may occur.
 
-<img alt="database diagram" src="https://github.com/user-attachments/assets/8625e58a-660b-47f7-8e01-ab74a1286617" />
+<img alt="database diagram" src="https://github.com/user-attachments/assets/cfde0cea-07fa-4538-8ebb-9d97b1c352cc" />
 
 ## Application Database