Definition 96.12.1. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids. Let $\mathcal{F}$ be a presheaf of $\mathcal{O}_\mathcal {X}$-modules. We say $\mathcal{F}$ is locally quasi-coherent1 if $\mathcal{F}$ is a sheaf for the étale topology and for every object $x$ of $\mathcal{X}$ the restriction $x^*\mathcal{F}|_{U_{\acute{e}tale}}$ is a quasi-coherent sheaf. Here $U = p(x)$.
[1] This is nonstandard notation.
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