The Stacks project

Lemma 48.11.3. With notation as above. The composition

\[ D(\mathcal{O}_ X) \xrightarrow {R\mathop{\mathcal{H}\! \mathit{om}}\nolimits (f_*\mathcal{O}_ Y, -)} D(f_*\mathcal{O}_ Y) \to D(\mathcal{O}_ X) \]

is the functor $K \mapsto R\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(f_*\mathcal{O}_ Y, K)$.

Proof. This is immediate from the construction. $\square$

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