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In a triangulated category with coproducts any idempotent splits.

Is there a proof of this fact different from that in Neeman, Prop. 1.6.8? In particular I'm looking for one which doesn't use the notion of homotopy colimit.

Thanks.

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    Here's an [MO thread](http://mathoverflow.net/questions/53006/how-do-i-split-a-homotopy-idempotent) on that argument.2011-12-07

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