1. A morphism with a right inverse is called a split epimorphism . 2. It follows in particular that every cokernel is an epimorphism . 3. For example, the inclusion is a ring epimorphism , but not a surjection. 4. A morphism that is both a monomorphism and an epimorphism is called a bimorphism. 5. However, the two definitions of " epimorphism " are equivalent for modules. 6. Every localization is a ring epimorphism , which is not, in general, surjective. 7. A strong monomorphism satisfies a certain lifting property with respect to commutative squares involving an epimorphism . 8. There are many right inverses to string projection, and thus it is a split epimorphism . 9. A "'split epimorphism "'is an homomorphism that has a left inverse. 10. Every coequalizer is an epimorphism , a consequence of the uniqueness requirement in the definition of coequalizers.
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