The Stacks project

Definition 73.8.5. Let $S$ be a scheme. A big ph site $(\textit{Spaces}/S)_{ph}$ is any site constructed as follows:

  1. Choose a big ph site $(\mathit{Sch}/S)_{ph}$ as in Topologies, Section 34.8.

  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 ph coverings of Definition 73.8.1.

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