Image factorization in an abelian category
= Image factorization in an abelian category
{title2=$A\twoheadrightarrow\operatorname{im}f\hookrightarrow B$}
For a <morphism> in an <abelian category>, its <coimage> $\operatorname{coker}(\ker f)$ is canonically isomorphic to its image $\ker(\operatorname{coker}f)$. This yields an <epimorphism> followed by a <monomorphism>, unique up to unique compatible <isomorphism>. Every epi-mono factorization has this same middle object.