The Stacks project

Lemma 96.24.3. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids. Let $\tau \in \{ Zariski, {\acute{e}tale}, smooth, syntomic, fppf\} $. The functor $\mathcal{X}_{affine, \tau } \to \mathcal{X}_\tau $ is a special cocontinuous functor. Hence it induces an equivalence of topoi from $\mathop{\mathit{Sh}}\nolimits (\mathcal{X}_{affine, \tau })$ to $\mathop{\mathit{Sh}}\nolimits (\mathcal{X}_\tau )$.

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