Proposition 22.27.16. In Situation 22.27.2 the homotopy category K(\mathcal{A}) with its natural translation functors and distinguished triangles is a triangulated category.
Proof. By Lemma 22.27.14 we know that K(\mathcal{A}) is pre-triangulated. Combining Lemmas 22.27.7 and 22.27.15 with Derived Categories, Lemma 13.4.15, we conclude that K(\mathcal{A}) is a triangulated category. \square
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