Lemma 35.2.4. Let S be a scheme. Let S = \bigcup U_ i be an open covering. Any descent datum on quasi-coherent sheaves for the family \mathcal{U} = \{ U_ i \to S\} is effective. Moreover, the functor from the category of quasi-coherent \mathcal{O}_ S-modules to the category of descent data with respect to \mathcal{U} is fully faithful.
Proof. This follows immediately from Sheaves, Section 6.33 and the fact that being quasi-coherent is a local property, see Modules, Definition 17.10.1. \square
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