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Epimorphism
algebra define an epimorphism simply as an onto or surjective homomorphism. Every epimorphism in this algebraic sense is an epimorphism in the sense of
Morphism
always epimorphisms, but the converse is not true in general, as an epimorphism may fail to have a right inverse. A split epimorphism is an epimorphism having
Homomorphism
split epimorphism is always an epimorphism, for both meanings of epimorphism. For sets and vector spaces, every epimorphism is a split epimorphism, but
Section (category theory)
and retractions are also called split epimorphisms. In an abelian category, if f : X → Y is a split epimorphism with split monomorphism g : Y → X, then
Surjective function
ἐπί meaning over, above, on. Any morphism with a right inverse is an epimorphism, but the converse is not true in general. A right inverse g of a morphism
Normal morphism
is one in which every epimorphism is conormal. A monomorphism is normal if it is the kernel of some morphism, and an epimorphism is conormal if it is the
Monomorphism
categorical dual of a monomorphism is an epimorphism, that is, a monomorphism in a category C is an epimorphism in the dual category Cop. Every section
Ring homomorphism
homomorphisms are vastly different from epimorphisms in the category of rings. For example, the inclusion Z ⊆ Q is a ring epimorphism, but not a surjection. However
Morphine
Morphine is a pain medication of the opiate family which is found naturally in a number of plants and animals, including humans. It acts directly on the
Five lemma
commutative diagram are exact and m and p are epimorphisms and q is a monomorphism, then n is an epimorphism. (2) If the rows in the commutative diagram