Lemma 95.5.3. There exists a subcategory $\mathcal{QC}\! \mathit{oh}_{fg, small} \subset \mathcal{QC}\! \mathit{oh}_{fg}$ with the following properties:

the inclusion functor $\mathcal{QC}\! \mathit{oh}_{fg, small} \to \mathcal{QC}\! \mathit{oh}_{fg}$ is fully faithful and essentially surjective, and

the functor $p_{fg, small} : \mathcal{QC}\! \mathit{oh}_{fg, small} \to (\mathit{Sch}/S)_{fppf}$ turns $\mathcal{QC}\! \mathit{oh}_{fg, small}$ into a stack over $(\mathit{Sch}/S)_{fppf}$.

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