Section 95.10 (0305): The stack associated to a sheaf

95.10 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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The Stacks project

95.10 The stack associated to a sheaf

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