The Stacks project

Lemma 15.60.3. Let $R \to A$ be a ring map. The functor $D(R) \to D(A)$, $E \mapsto E \otimes _ R^\mathbf {L} A$ of Lemma 15.60.1 is left adjoint to the restriction functor $D(A) \to D(R)$.

Proof. This follows from Derived Categories, Lemma 13.30.1 and the fact that $- \otimes _ R A$ and restriction are adjoint by Algebra, Lemma 10.14.3. $\square$

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