Lemma 82.3.1. Let $S$ be a scheme. Let $\tau \in \{ {\acute{e}tale}, fppf, ph\} $ (add more here). The inclusion functor

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

Lemma 82.3.1. 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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