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