Lemma 34.10.6. Let $T$ be an affine scheme. Let $\{ T_ j \to T\} _{j = 1, \ldots , m}$ be a family of morphisms with $T_ j$ affine for all $j$. The following are equivalent

$\{ T_ j \to T\} _{j = 1, \ldots , m}$ is a standard V covering,

there is a standard V covering which refines $\{ T_ j \to T\} _{j = 1, \ldots , m}$, and

$\{ \coprod _{j = 1, \ldots , m} T_ j \to T\} $ is a standard V covering.

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