The Stacks project

Lemma 20.26.8. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of ringed spaces. The pullback of a K-flat complex of $\mathcal{O}_ Y$-modules is a K-flat complex of $\mathcal{O}_ X$-modules.

Proof. We can check this on stalks, see Lemma 20.26.4. Hence this follows from Sheaves, Lemma 6.26.4 and More on Algebra, Lemma 15.59.3. $\square$

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