The Stacks project

Definition 61.12.14. In the situation of Lemma 61.12.13 the functor $i_ S^{-1} = \pi _{S, *}$ is often called the restriction to the small pro-étale site, and for a sheaf $\mathcal{F}$ on the big pro-étale site we denote $\mathcal{F}|_{S_{pro\text{-}\acute{e}tale}}$ this restriction.