The Stacks project

Lemma 21.18.6. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $(\mathcal{K}_1^\bullet , \mathcal{K}_2^\bullet , \mathcal{K}_3^\bullet )$ be a distinguished triangle in $K(\textit{Mod}(\mathcal{O}))$. If two out of three of $\mathcal{K}_ i^\bullet $ are K-flat, so is the third.

Proof. Follows from Lemma 21.18.1 and the fact that in a distinguished triangle in $K(\textit{Mod}(\mathcal{O}))$ if two out of three are acyclic, so is the third. $\square$


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