Lemma 38.34.8. 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
$\{ T_ i \to T\} _{i \in I}$ is an h covering,
there is an h covering which refines $\{ T_ i \to T\} _{i \in I}$, and
$\{ \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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