The Stacks project

Definition 34.8.4. Let $T$ be a scheme. A ph covering of $T$ is a family of morphisms $\{ f_ i : T_ i \to T\} _{i \in I}$ of schemes such that $f_ i$ is locally of finite type and such that for every affine open $U \subset T$ there exists a standard ph covering $\{ U_ j \to U\} _{j = 1, \ldots , m}$ refining the family $\{ T_ i \times _ T U \to U\} _{i \in I}$.