The Stacks project

Example 90.11.10. Since $\mathcal{C}_\Lambda $ contains all $k[V]$ for finite dimensional vector spaces $V$ we see that Definition 90.11.9 applies with $S = \Lambda $, $R = k$, $\mathcal{C} = \mathcal{C}_\Lambda $, and $F : \mathcal{C}_\Lambda \to \textit{Sets}$ a predeformation functor. The tangent space is $TF = F(k[\epsilon ])$.