Definition 66.18.7. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. The *étale topos* of $X$, or more precisely the *small étale topos* of $X$ is the category $\mathop{\mathit{Sh}}\nolimits (X_{\acute{e}tale})$ of sheaves of sets on $X_{\acute{e}tale}$.

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