Lemma 15.91.9 (0A6C)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.91: Derived Completion
Lemma 15.91.9 (cite)

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Lemma 15.91.9. Let $A$ be a ring. Let $f, g \in A$ . Then for $K \in D(A)$ we have $R\mathop{\mathrm{Hom}}\nolimits _ A(A_ f, R\mathop{\mathrm{Hom}}\nolimits _ A(A_ g, K)) = R\mathop{\mathrm{Hom}}\nolimits _ A(A_{fg}, K)$ .

Proof. This follows from Lemma 15.73.1. $\square$

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