Lemma 6.24.5 (008W)—The Stacks project

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Part 1: Preliminaries
Chapter 6: Sheaves on Spaces
Section 6.24: Continuous maps and sheaves of modules
Lemma 6.24.5 (cite)

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Lemma 6.24.5. Let $f : X \to Y$ be a continuous map of topological spaces. Let $\mathcal{O}$ be a sheaf of rings on $X$ . Let $\mathcal{F}$ be a sheaf of $\mathcal{O}$ -modules. The pushforward $f_*\mathcal{F}$ , as defined in Lemma 6.24.1 is a sheaf of $f_*\mathcal{O}$ -modules.

Proof. Obvious from the definition and Lemma 6.21.1. $\square$

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