The Stacks project

Lemma 38.34.7. Let $T$ be a scheme. Let $\{ f_ i : T_ i \to T\} _{i \in I}$ be a family of morphisms such that $f_ i$ is locally of finite presentation for all $i$. The following are equivalent

  1. $\{ T_ i \to T\} _{i \in I}$ is an h covering,

  2. there is an h covering which refines $\{ T_ i \to T\} _{i \in I}$, and

  3. $\{ \coprod _{i \in I} T_ i \to T\} $ is an h covering.

Proof. This follows from the analogous statement for ph coverings (Topologies, Lemma 34.8.7) or from the analogous statement for V coverings (Topologies, Lemma 34.10.8). $\square$


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