The Stacks project

Lemma 115.8.4. Let $(\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C})$ be a ringed topos. For any complex of $\mathcal{O}_\mathcal {C}$-modules $\mathcal{G}^\bullet $ there exists a quasi-isomorphism $\mathcal{K}^\bullet \to \mathcal{G}^\bullet $ such that $f^*\mathcal{K}^\bullet $ is a K-flat complex of $\mathcal{O}_\mathcal {D}$-modules for any morphism $f : (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}_\mathcal {D}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}_\mathcal {C})$ of ringed topoi.

Proof. This follows from Cohomology on Sites, Lemmas 21.17.11 and 21.18.1. $\square$

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