Remark 56.4.4. Combining Remarks 56.3.10 and 56.4.2 and Lemma 56.4.3 we find the following. Given rings $A$ and $B$ the set of ring maps $A \to B$ is in bijection with the set of isomorphism classes of functors of monoidal categories $\text{Mod}^{fp}_ A \to \text{Mod}^{fp}_ B$ which are right exact.

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