Is every balanced pre-abelian category abelian? That is, given an additive category $\mathcal{A}$ in which cokernels and kernels exists, such that every morphism, which is a mono- and an epimorphism, is an isomorphism; does it follow that $\mathcal{A}$ is abelian? Note that it would suffice to prove that the canonical morphism $coim(f) \to im(f)$, where $f$ is an arbitrary morphism, is a mono- and an epimorphism.

Note that the usual examples for non-abelian categories somehow suggest this (filtered modules, topological abelian groups). See also this related question.

After a google search I have found the following theorem (in "Basic homological algebra" by M. Scott Osborne, Cor. 7.18): If $\mathcal{A}$ is a balanced pre-abelian category with a separating class of projectives and a coseparating class of injectives, then $\mathcal{A}$ is abelian. Ok then this does not seem to be true in general. Does anybody know an example?