Remark 20.42.13. Let $h : X \to Y$ be a morphism of ringed spaces. Let $K, L$ be objects of $D(\mathcal{O}_ Y)$. We claim there is a canonical map

in $D(\mathcal{O}_ X)$. Namely, by (20.42.0.1) proved in Lemma 20.42.2 such a map is the same thing as a map

The source of this arrow is $Lh^*(\mathop{\mathcal{H}\! \mathit{om}}\nolimits (K, L) \otimes ^\mathbf {L} K)$ by Lemma 20.27.3 hence it suffices to construct a canonical map

For this we take the arrow corresponding to

via (20.42.0.1).

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