Lemma 47.13.1. Let $A \to B$ be a ring homomorphism. The functor $R\mathop{\mathrm{Hom}}\nolimits (B, -)$ constructed above is right adjoint to the restriction functor $D(B) \to D(A)$.

**Proof.**
This is a consequence of the fact that restriction and $\mathop{\mathrm{Hom}}\nolimits _ A(B, -)$ are adjoint functors by Algebra, Lemma 10.13.4. See Derived Categories, Lemma 13.30.3.
$\square$

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