Add functor properties: preserve regular epis / monos#262
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…move several redundant assignments
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Two new properties of functors are added:
The properties have been decided for all functors.
A couple of implications have been added as well. For example, a functor preserving equalizers of course also preserves regular monomorphisms. The most useful result is the following, as it also made several previous assignments redundant: Let$C$ be a category with pushouts. A functor $C \to D$ preserving coreflexive equalizers already preserves regular monomorphisms. Thus, if $C$ is mono-regular, the functor also preserves monomorphisms. And as usual, this dualizes as well.
Also, a small bug in the generation of contradiction proofs for functors has been fixed.