Remark 20.42.14. Suppose that

is a commutative diagram of ringed spaces. Let $K, L$ be objects of $D(\mathcal{O}_ X)$. We claim there exists a canonical base change map

in $D(\mathcal{O}_{S'})$. Namely, we take the map adjoint to the composition

where the first arrow uses the adjunction mapping $Lf^*Rf_* \to \text{id}$ and the second arrow is the canonical map constructed in Remark 20.42.13.

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