The Stacks project

Lemma 84.3.1. Let $S$ be a scheme. Let $\tau \in \{ {\acute{e}tale}, fppf, ph\} $ (add more here). The inclusion functor

\[ (\mathit{Sch}/S)_\tau \longrightarrow (\textit{Spaces}/S)_\tau \]

is a special cocontinuous functor (Sites, Definition 7.29.2) and hence identifies topoi.

Proof. The conditions of Sites, Lemma 7.29.1 are immediately verified as our functor is fully faithful and as every algebraic space has an étale covering by schemes. $\square$

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