The Stacks project

Definition 98.12.2. Let $S$ be a locally Noetherian scheme. Let $\mathcal{X}$ be fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Let $U$ be a scheme locally of finite type over $S$. Let $x$ be an object of $\mathcal{X}$ lying over $U$. Let $u_0$ be finite type point of $U$. We say $x$ is versal at $u_0$ if the morphism $\hat x$ (98.12.1.1) is smooth, see Formal Deformation Theory, Definition 90.8.1.