Monomorphism

up:: Category

A monomorphism is a categorical generalization of an Injective Function, since An injective function is a monomorphism in the category Set.

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

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

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

Related

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

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References

• monomorphism in nLab