Definition 94.11.1. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids. A quasi-coherent module on $\mathcal{X}$, or a quasi-coherent $\mathcal{O}_\mathcal {X}$-module is a quasi-coherent module on the ringed site $(\mathcal{X}_{fppf}, \mathcal{O}_\mathcal {X})$ as in Modules on Sites, Definition 18.23.1. The category of quasi-coherent sheaves on $\mathcal{X}$ is denoted $\mathit{QCoh}(\mathcal{O}_\mathcal {X})$.

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