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How can I prove that additive functors preserve split exact sequences?

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Prove that a split exact sequence $0 \to A \to B \to C \to 0$ is isomorphic to the obvious direct sum sequence $0 \to A \to A \oplus C \to C \to 0$. –  t.b. Apr 18 '12 at 8:41
(Prove also that a functor is additive if and only if it preserves 0 and binary direct sums.) –  Zhen Lin Apr 18 '12 at 8:42
@ZhenLin Please consider converting your comment (and the comment by t.b.) into a (hint only) answer, so that this question gets removed from the unanswered tab. If you do so, it is helpful to post it to this chat room to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see here, here or here. –  Julian Kuelshammer Jun 18 '13 at 17:25

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