The Stacks project

Lemma 59.64.2. Let $f : X \to Y$ be a morphism of schemes. If $\mathcal{G}$ is a locally constant sheaf of sets, abelian groups, or $\Lambda $-modules on $Y_{\acute{e}tale}$, the same is true for $f^{-1}\mathcal{G}$ on $X_{\acute{e}tale}$.

Proof. Holds for any morphism of topoi, see Modules on Sites, Lemma 18.43.2. $\square$

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