The Stacks project

Definition 73.4.5. Let $S$ be a scheme. A big étale site $(\textit{Spaces}/S)_{\acute{e}tale}$ is any site constructed as follows:

  1. Choose a big étale site $(\mathit{Sch}/S)_{\acute{e}tale}$ as in Topologies, Section 34.4.

  2. As underlying category take the category $\textit{Spaces}/S$ of algebraic spaces over $S$ (see discussion in Section 73.2 why this is a set).

  3. Choose any set of coverings as in Sets, Lemma 3.11.1 starting with the category $\textit{Spaces}/S$ and the class of étale coverings of Definition 73.4.1.

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