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Add strong epimorphisms and strong monomorphisms#296

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ScriptRaccoon merged 3 commits into
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strong-epis
Jul 17, 2026
Merged

Add strong epimorphisms and strong monomorphisms#296
ScriptRaccoon merged 3 commits into
mainfrom
strong-epis

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@ScriptRaccoon ScriptRaccoon commented Jul 17, 2026

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This PR implements another part of #267 by adding strong epimorphisms and strong monomorphisms.

Basic results are added (and as usual, they are dualized automatically):

  • strict mono ===> strong mono ===> mono
  • epi + strong mono ===> iso
  • in coregular categories: strong mono ===> regular mono
  • in quotient-trivial categories: monomorphism ===> strong monomorphism

This has already decided the properties for all (well, there are not so many) morphisms in the database.

Moreover, an example of a strong epimorphism which is not strict (and hence, not regular) has been added, the evident functor IIdem as a morphism in Cat.

This is unrelated to the new properties, but the universal morphism has been added as well.

@ScriptRaccoon
ScriptRaccoon merged commit 8afc84c into main Jul 17, 2026
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ScriptRaccoon deleted the strong-epis branch July 17, 2026 18:55
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