The Stacks project

Lemma 20.26.6. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $(\mathcal{K}_1^\bullet , \mathcal{K}_2^\bullet , \mathcal{K}_3^\bullet )$ be a distinguished triangle in $K(\textit{Mod}(\mathcal{O}_ X))$. If two out of three of $\mathcal{K}_ i^\bullet $ are K-flat, so is the third.

Proof. Follows from Lemma 20.26.1 and the fact that in a distinguished triangle in $K(\textit{Mod}(\mathcal{O}_ X))$ if two out of three are acyclic, so is the third. $\square$

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