Definition 34.4.6. A *big étale site* is any site $\mathit{Sch}_{\acute{e}tale}$ as in Sites, Definition 7.6.2 constructed as follows:

Choose any set of schemes $S_0$, and any set of étale coverings $\text{Cov}_0$ among these schemes.

As underlying category take any category $\mathit{Sch}_\alpha $ constructed as in Sets, Lemma 3.9.2 starting with the set $S_0$.

Choose any set of coverings as in Sets, Lemma 3.11.1 starting with the category $\mathit{Sch}_\alpha $ and the class of étale coverings, and the set $\text{Cov}_0$ chosen above.

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