The Stacks project

Lemma 13.31.3. Let $\mathcal{A}$ be an abelian category. Let $(K, L, M, f, g, h)$ be a distinguished triangle of $K(\mathcal{A})$. If two out of $K$, $L$, $M$ are K-injective complexes, then the third is too.

Proof. Follows from the definition, Lemma 13.4.2, and the fact that $K(\mathcal{A})$ is a triangulated category (Proposition 13.10.3). $\square$

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