Monomorphism

Summary

A monomorphism is a morphism $f$ that can be cancelled on the left: $f \circ g_1 = f \circ g_2$ implies $g_1 = g_2$. It is the categorical version of an injective function. In the categories of sets, groups, rings and vector spaces, the monomorphisms are exactly the injective homomorphisms. Its dual notion is the epimorphism.