CatDat

normal epimorphism

A morphism $f : A \to B$ in a category with zero morphisms is a normal epimorphism if it is the cokernel of a morphism $g : C \to A$, i.e. the coequalizer of $g$ and the zero morphism $0 : C \to A$.

• Dual property: normal monomorphism
• Related properties: regular epimorphism
• nLab Link

Relevant implications

• isomorphism () implies normal epimorphism
• normal epimorphism implies regular epimorphism
• regular epimorphism () implies normal epimorphism

Examples

There are 3 morphisms with this property.

• identity map of a group
• reduction modulo p
• universal split epimorphism

Counterexamples

There are 10 morphisms without this property.

• Baer-Specker relations
• embedding of A3 into S3
• embedding of integer into rational numbers
• handle of the universal fork
• identity map of a set
• map from the empty set
• map into the singleton set
• multiplication with 2
• presentation of the walking idempotent
• universal morphism

Unknown

There are 0 morphisms for which the database has no information on whether they satisfy this property.

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