Lemma 21.17.6. 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 21.17.1 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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