Epimorphism

up:: Category

An epimorphism is a generalization of a Surjective Function, since A surjective function is an epimorphism in the category Set.

Given a category $C$ and a morphism $f\in Hom(X,Y)$, we say that $f$ is an epimorphism if

$$\forall g_1,g_2\in Hom(Y,Z):(g_1\circ f=g_2\circ f)⟹g_1=g_2$$

That is, if they are “equal” after composing with $f$, then they were equal all along.

Related

• Epimorphisms in $C$ are Monomorphisms in the Opposite Category $C^{op}$.

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References

• epimorphism in nLab