Lemma 96.3.3. Let $S$ be a locally Noetherian scheme. Let

be a $2$-fibre product of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Let $k$ be a finite type field over $S$ and $w_0$ an object of $\mathcal{W}$ over $k$. Let $x_0, z_0, y_0$ be the images of $w_0$ under the morphisms in the diagram. Then

is a fibre product of predeformation categories.

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