Lemma 90.11.15. Let $F: \mathcal{C} \to \textit{Sets}$ be a functor satisfying the hypotheses of Lemma 90.11.8. 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 90.11.6.
$\square$

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