The Stacks project

Definition 34.4.15. In the situation of Lemma 34.4.14 the functor $i_ S^{-1} = \pi _{S, *}$ is often called the restriction to the small étale site, and for a sheaf $\mathcal{F}$ on the big étale site we denote $\mathcal{F}|_{S_{\acute{e}tale}}$ this restriction.

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