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The Stacks project

Definition 34.5.6. A big smooth site is any site $\mathit{Sch}_{smooth}$ as in Sites, Definition 7.6.2 constructed as follows:

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

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

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

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