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Add normal epimorphisms and normal monomorphisms#292

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ScriptRaccoon merged 8 commits into
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normal-epis
Jul 16, 2026
Merged

Add normal epimorphisms and normal monomorphisms#292
ScriptRaccoon merged 8 commits into
mainfrom
normal-epis

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@ScriptRaccoon ScriptRaccoon commented Jul 16, 2026

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This PR implements another part of #267 by adding normal epimorphisms and normal monomorphisms. These are only defined in categories with zero morphisms.

Their basic properties are added (every normal epi is regular, etc.), and also examples showing that some implications are not true:

  • the embedding $A_3 \hookrightarrow S_3$ in Grp is an example of a normal monomorphism that does not split
  • the projection $Z \to Z/p$ in Ab is an example of a normal epimorphism that does not split
  • the multiplication $2 : Z \to Z$ in TorsFreeAb is an example of a monomorphism (and epimorphism) in an additive category that is not normal

Because of the two new properties, the identity morphism idX in Set (for a set X) does not have all properties of morphisms anymore. Therefore, also the identity morphism idG in Grp (for a group G) has been added. It has all current properties. This is also verified in the test script.

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ScriptRaccoon marked this pull request as ready for review July 16, 2026 16:57
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ScriptRaccoon merged commit cc46e9d into main Jul 16, 2026
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ScriptRaccoon deleted the normal-epis branch July 16, 2026 17:17
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