Image and coimage in an abelian category ($\mathrm{im}f,\mathrm{coim}f$)

For $f:A\to B$ in an abelian category,The canonical morphism $\mathrm{coim}f\to \mathrm{im}f$ is an isomorphism, giving the canonical epimorphism--isomorphism--monomorphism factorization of $f$.