Remark 20.42.10. Let $(X, \mathcal{O}_ X)$ be a ringed space. For $K, K', M, M'$ in $D(\mathcal{O}_ X)$ there is a canonical map

Namely, by (20.42.0.1) is the same thing as a map

For this we can first flip the middle two factors (with sign rules as in More on Algebra, Section 15.72) and use the maps

from Lemma 20.42.5 when thinking of $K = R\mathop{\mathcal{H}\! \mathit{om}}\nolimits (\mathcal{O}_ X, K)$ and similarly for $K'$, $M$, and $M'$.

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