The Stacks project

Remark 98.9.2. Let $S$ be a locally Noetherian scheme. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids. Let $\xi = (R, \xi _ n, f_ n)$ be a formal object. Set $k = R/\mathfrak m$ and $x_0 = \xi _1$. The formal object $\xi$ defines a formal object $\xi$ of the predeformation category $\mathcal{F}_{\mathcal{X}, k, x_0}$. This follows immediately from Definition 98.9.1 above, Formal Deformation Theory, Definition 90.7.1, and our construction of the predeformation category $\mathcal{F}_{\mathcal{X}, k, x_0}$ in Section 98.3.