Lemma 89.11.15. Let $F: \mathcal{C} \to \textit{Sets}$ be a functor satisfying the hypotheses of Lemma 89.11.8. Assume $R = K$ is a field. Then $F(K[V]) \cong TF \otimes _ K V$ for any finite dimensional $K$-vector space $V$.

Proof. Follows from Lemma 89.11.6. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).