Definition 98.5.1. Let $S$ be a locally Noetherian scheme. Let $\mathcal{Z}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. We say $\mathcal{Z}$ satisfies condition (RS) if for every pushout
\[ \xymatrix{ X \ar[r] \ar[d] & X' \ar[d] \\ Y \ar[r] & Y' = Y \amalg _ X X' } \]
in the category of schemes over $S$ where
$X$, $X'$, $Y$, $Y'$ are spectra of local Artinian rings,
$X$, $X'$, $Y$, $Y'$ are of finite type over $S$, and
$X \to X'$ (and hence $Y \to Y'$) is a closed immersion
the functor of fibre categories
\[ \mathcal{Z}_{Y'} \longrightarrow \mathcal{Z}_ Y \times _{\mathcal{Z}_ X} \mathcal{Z}_{X'} \]
is an equivalence of categories.
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