Lemma 21.18.7 (0DEP)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 21: Cohomology on Sites
Section 21.18: Derived pullback
Lemma 21.18.7 (cite)

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Lemma 21.18.7. Let $f : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}'), \mathcal{O}')$ be a morphism of ringed topoi. If $\mathcal{C}$ has enough points, then the pullback of a K-flat complex of $\mathcal{O}'$ -modules is a K-flat complex of $\mathcal{O}$ -modules.

Proof. This follows from Lemma 21.18.6, Modules on Sites, Lemma 18.36.4, and More on Algebra, Lemma 15.59.3. $\square$

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