Zero-cokernel criterion for epimorphisms
= Zero-cokernel criterion for epimorphisms
In an <abelian category>, a morphism is an <epimorphism> if and only if its <categorical cokernel> object is zero. For the reverse implication, any difference of maps annihilating the morphism factors through its cokernel and is therefore zero. The <cokernel invariance under pushout> then proves both preservation and reflection of epimorphisms by pushout.