Lemma 56.4.1. Let $A$ and $B$ be rings. Let $F : \text{Mod}^{fp}_ A \to \text{Mod}^{fp}_ B$ be a functor. Then $F$ extends uniquely to a functor $F' : \text{Mod}_ A \to \text{Mod}_ B$ which commutes with filtered colimits.

**Proof.**
Special case of Lemma 56.2.1.
$\square$

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