Lemma 66.29.2 (03GA)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 66: Properties of Algebraic Spaces
Section 66.29: Quasi-coherent sheaves on algebraic spaces
Lemma 66.29.2 (cite)

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Lemma 66.29.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. The pullback functor $f^* : \textit{Mod}(\mathcal{O}_ Y) \to \textit{Mod}(\mathcal{O}_ X)$ preserves quasi-coherent sheaves.

Proof. This is a general fact, see Modules on Sites, Lemma 18.23.4. $\square$

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