Lemma 34.9.3. Let $T$ be a scheme. Let $\{ f_ i : T_ i \to T\} _{i \in I}$ be a family of morphisms of schemes with target $T$. The following are equivalent

$\{ f_ i : T_ i \to T\} _{i \in I}$ is an fpqc covering, and

setting $T' = \coprod _{i \in I} T_ i$, and $f = \coprod _{i \in I} f_ i$ the family $\{ f : T' \to T\} $ is an fpqc covering.

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