11. The converse, namely that every epimorphism be a coequalizer, is not true in all categories. 12. He held that from his theory of " epimorphism " evolution is a directed process. 13. Any morphism with a right inverse is an epimorphism , but the converse is not true in general. 14. In short, the property of being a monomorphism is dual to the property of being an epimorphism . 15. In this article, the term " epimorphism " will be used in the sense of category theory given above. 16. In many categories it is possible to write every morphism as the composition of an epimorphism followed by a monomorphism. 17. This is also an example of a ring homomorphism which is both a monomorphism and an epimorphism , but not an isomorphism. 18. A "'regular epimorphism "'is an epimorphism which appears as a coequalizer of some pair of morphisms. 19. A "'regular epimorphism "'is an epimorphism which appears as a coequalizer of some pair of morphisms. 20. For sets and vector spaces, every epimorphism is a split epimorphism, but this property is wrong for most common algebraic structures.
