In category theory, an **epimorphism** (also called an **epic morphism** or, colloquially, an **epi**) is a morphism *f* : *X* → *Y* which is right-cancellative in the sense that, for all morphisms *g*_{1}, *g*_{2} : *Y* → *Z*,

Epimorphisms are analogues of surjective functions, but they are not exactly the same. The dual of an epimorphism is a monomorphism (i.e. an epimorphism in a category *C* is a monomorphism in the dual category *C*op).

Many authors in abstract algebra and universal algebra define an **epimorphism** simply as an *onto* or surjective homomorphism. Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories. In this article, the term "epimorphism" will be used in the sense of category theory given above. For more on this, see the section on Terminology below.

Read more about Epimorphism: Examples, Properties, Related Concepts, Terminology

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