Lemma 17.16.2 (05NA)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 17: Sheaves of Modules
Section 17.16: Tensor product
Lemma 17.16.2 (cite)

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Lemma 17.16.2. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}'$ , $\mathcal{G}'$ be presheaves of $\mathcal{O}_ X$ -modules with sheafifications $\mathcal{F}$ , $\mathcal{G}$ . Then $\mathcal{F} \otimes _{\mathcal{O}_ X} \mathcal{G} = (\mathcal{F}' \otimes _{p, \mathcal{O}_ X} \mathcal{G}')^\#$ .

Proof. Omitted. $\square$

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