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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