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