Proposition 22.20.16. In Situation 22.20.2 the homotopy category $K(\mathcal{A})$ with its natural translation functors and distinguished triangles is a triangulated category.

Proof. By Lemma 22.20.14 we know that $K(\mathcal{A})$ is pre-triangulated. Combining Lemmas 22.20.7 and 22.20.15 with Derived Categories, Lemma 13.4.14, we conclude that $K(\mathcal{A})$ is a triangulated category. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).