Page "Epimorphism" Paragraph 4

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.