Lemma 54.21.4. Let $S$ be a scheme. Let $S_{affine, Zar}$ denote the full subcategory of $S_{Zar}$ consisting of affine objects. A covering of $S_{affine, Zar}$ will be a standard Zariski covering, see Topologies, Definition 33.3.4. Then restriction
defines an equivalence of topoi $\mathop{\mathit{Sh}}\nolimits (S_{Zar}) \cong \mathop{\mathit{Sh}}\nolimits (S_{affine, Zar})$.
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