The Stacks project

Lemma 73.3.4. Let $S$ be a scheme. Let $U$ be an algebraic space over $S$. Let $\{ U_ i \to U\} $ be a Zariski covering of $U$, see Topologies on Spaces, Definition 72.3.1. Any descent datum on quasi-coherent sheaves for the family $\mathcal{U} = \{ U_ i \to U\} $ is effective. Moreover, the functor from the category of quasi-coherent $\mathcal{O}_ U$-modules to the category of descent data with respect to $\{ U_ i \to U\} $ is fully faithful.

Proof. Omitted. $\square$


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