The Stacks project

Lemma 78.27.2. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $G$ be a group algebraic space over $B$. Endow $B$ with the trivial action of $G$. The morphism

\[ [B/G] \longrightarrow \mathcal{S}_ B \]

(Lemma 78.20.2) turns $[B/G]$ into a gerbe over $B$.

Proof. Immediate from Lemma 78.27.1 as the morphisms $B \to B$ and $B \times _ B G \to B$ are surjective as morphisms of sheaves. $\square$

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