Remark 89.11.2. One can define the notion of an $R$-linearity for any functor between categories enriched over $\text{Mod}_ R$. We made the definition specifically for functors $L: \text{Mod}^{fg}_ R \to \text{Mod}_ R$ and $L: \text{Mod}_ R \to \text{Mod}_ R$ because these are the cases that we have needed so far.

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