The Stacks project

Definition 73.4.9. In the situation of Lemma 73.4.8 the functor $i_ X^{-1} = \pi _{X, *}$ is often called the restriction to the small étale site, and for a sheaf $\mathcal{F}$ on the big étale site we often denote $\mathcal{F}|_{X_{\acute{e}tale}}$ this restriction.