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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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