# Normal epimorphism

From Encyclopedia of Mathematics

A morphism having the characteristic property of the natural mapping of a group onto a quotient group or of a ring onto a quotient ring. Let be a category with zero morphisms. A morphism is called a normal epimorphism if every morphism for which it always follows from , , that , can be uniquely represented in the form . The cokernel of any morphism is a normal epimorphism. The converse assertion is false, in general; however, when morphisms in have kernels, then every normal epimorphism is a cokernel. In an Abelian category every epimorphism is normal. The concept of a normal epimorphism is dual to that of a normal monomorphism.

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Normal epimorphism.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Normal_epimorphism&oldid=15791

This article was adapted from an original article by M.Sh. Tsalenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article