The Stacks project

Definition 98.18.1. Let $S$ be a scheme. Let $\mathcal{X}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. We say $\mathcal{X}$ satisfies condition (RS*) if given a fibre product diagram

\[ \xymatrix{ B' \ar[r] & B \\ A' = A \times _ B B' \ar[u] \ar[r] & A \ar[u] } \]

of $S$-algebras, with $B' \to B$ surjective with square zero kernel, the functor of fibre categories

\[ \mathcal{X}_{\mathop{\mathrm{Spec}}(A')} \longrightarrow \mathcal{X}_{\mathop{\mathrm{Spec}}(A)} \times _{\mathcal{X}_{\mathop{\mathrm{Spec}}(B)}} \mathcal{X}_{\mathop{\mathrm{Spec}}(B')} \]

is an equivalence of categories.

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