epimorphism in a sentence

Examples

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