A morphism in a category is an epimorphism if, for any two morphisms , implies . 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.

# Epimorphism

## See also

Category, Monomorphism, Morphism, Surjection## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Epimorphism." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Epimorphism.html