: Mathematics: epimorphism

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epimorphism

In category theory, an epimorphism is a morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms g₁, g₂: Y → Z,
${\\displaystyle g_{1}\\circ f=g_{2}\\circ f\\implies g_{1}=g_{2}.}$
Epimorphisms are categorical analogues of onto or surjective functions (and in the category of sets the concept corresponds exactly to the surjective functions), but they may not exactly coincide in all contexts; for example, the inclusion ${\\displaystyle \\mathbb {Z} \ o \\mathbb {Q} }$ is a ring epimorphism. The dual of an epimorphism is a monomorphism (i.e. an epimorphism in a category C is a monomorphism in the dual category C^op).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Epimorphism)

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