The Stacks project

Example 90.15.3. There exist predeformation categories which have a versal formal object satisfying (90.15.0.2) but which do not satisfy (S2). A quick example is to take $F = \underline{k[\epsilon ]}/G$ where $G \subset \text{Aut}_{\mathcal{C}_\Lambda }(k[\epsilon ])$ is a finite nontrivial subgroup. Namely, the map $\underline{k[\epsilon ]} \to F$ is smooth, but the tangent space of $F$ does not have a natural $k$-vector space structure (as it is a quotient of a $k$-vector space by a finite group).