Lemma 47.13.2. Let $A \to B \to C$ be ring maps. Then $R\mathop{\mathrm{Hom}}\nolimits (C, -) \circ R\mathop{\mathrm{Hom}}\nolimits (B, -) : D(A) \to D(C)$ is the functor $R\mathop{\mathrm{Hom}}\nolimits (C, -) : D(A) \to D(C)$.

**Proof.**
Follows from uniqueness of right adjoints and Lemma 47.13.1.
$\square$

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