Morphism

Regular epimorphism

A regular epimorphism is a morphism out of some object which occurs as the coëqualizer of some parallel pair of morphisms into . cat In particular by the universal property of the coëqualizer it is an epimorphism.

Proof

Let and be their equalizer. Let so that . Since the universal property demands the factorization of via be unique, it follows that .

See Regular monomorphism for the dual notion.

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