A morphism f:Y->X in a category is an epimorphism if, for any two morphisms u,v:X->Z, uf=vf implies u=v. In the categories of sets, groups, modules, etc., an epimorphism is the same as a surjection, and is used synonymously with "surjection" outside of category theory.

See also

Category, Monomorphism, Morphism, Surjection

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Cite this as:

Weisstein, Eric W. "Epimorphism." From MathWorld--A Wolfram Web Resource.

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