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Let $C$ be a pre-additive category with a zero object $O$. Suppose that every morphism in $C$ has a kernel and a cokernel and that every monomorphism in $C$ is a kernel of some morphism. Prove that every morphism $f$ in $C$ can be written as $hg$ for some epimorphism $g$ and monomorphism $h$.

How to prove it? I have no way to solve. Thanks.

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The formal dual of the proof given here works. –  Zhen Lin Nov 6 '13 at 9:56
@Zhen: Isn't this an answer? –  Martin Brandenburg Nov 9 '13 at 21:25

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