Lemma 34.10.8. Let $T$ be a scheme. Let $\{ f_ i : T_ i \to T\} _{i \in I}$ be a family of morphisms. The following are equivalent

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

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

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

Proof. Omitted. Hint: compare with the proof of Lemma 34.8.7. $\square$

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