## 94.10 The stack associated to a sheaf

Let $F : (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$ be a presheaf. We obtain a category fibred in sets

\[ p_ F : \mathcal{S}_ F \to (\mathit{Sch}/S)_{fppf}, \]

see Categories, Example 4.38.5. This is a stack in sets if and only if $F$ is a sheaf, see Stacks, Lemma 8.6.3.

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