Lemma 6.21.5 (008H)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 6: Sheaves on Spaces
Section 6.21: Continuous maps and sheaves
Lemma 6.21.5 (cite)

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Lemma 6.21.5. Let $x \in X$ . Let $\mathcal{G}$ be a sheaf of sets on $Y$ . There is a canonical bijection of stalks $(f^{-1}\mathcal{G})_ x = \mathcal{G}_{f(x)}$ .

Proof. This is a combination of Lemmas 6.17.2 and 6.21.4. $\square$

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