Lemma 90.11.13. Let F, G: \mathcal{C} \to \textit{Sets} be functors satisfying the hypotheses of Lemma 90.11.8. Let t : F \to G be a morphism of functors. For any M \in \mathop{\mathrm{Ob}}\nolimits (\text{Mod}^{fg}_ R), the map t_{R[M]}: F(R[M]) \to G(R[M]) is a map of R-modules, where F(R[M]) and G(R[M]) are given the R-module structure from Lemma 90.11.8. In particular, t_{R[\epsilon ]} : TF \to TG is a map of R-modules.
Proof. Follows from Lemma 90.11.5. \square
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