CatDat

normal monomorphism

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

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

Relevant implications

• isomorphism () implies normal monomorphism
• normal monomorphism implies regular monomorphism
• regular monomorphism () implies normal monomorphism

Examples

There are 2 morphisms with this property.

• embedding of A3 into S3
• identity map of a group

Counterexamples

There are 11 morphisms without this property.

• Baer-Specker relations
• 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
• reduction modulo p
• universal morphism
• universal split epimorphism

Unknown

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

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