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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