The Stacks project

Definition 34.8.9. A big ph site is any site $\mathit{Sch}_{ph}$ as in Sites, Definition 7.6.2 constructed as follows:

1. Choose any set of schemes $S_0$, and any set of ph 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 ph coverings, and the set $\text{Cov}_0$ chosen above.