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 Cop). Many authors in abstract algebra and universal algebra define an epimorphism simply as an onto or surjective homomorphism. Every epimor...
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http://en.wikipedia.org/wiki/Epimorphism
(from the article `homomorphism`) ...have their own names. A one-to-one homomorphism from to is called a monomorphism, and a homomorphism that is `onto,` or covers every element of ...
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http://www.britannica.com/eb/a-z/e/37
a homomorphism that maps from one set onto a second set.
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https://www.infoplease.com/dictionary/epimorphism
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