The Stacks project

Definition 59.15.5. Let $S$ be a scheme. The category of schemes over $S$ is denoted $\mathit{Sch}/S$. Consider a functor $\mathcal{F} : (\mathit{Sch}/S)^{opp} \to \textit{Sets}$, in other words a presheaf of sets. We say $\mathcal{F}$ satisfies the sheaf property for the fpqc topology if for every fpqc covering $\{ U_ i \to U\} _{i \in I}$ of schemes over $S$ the diagram (59.11.1.1) is an equalizer diagram.

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