Remark 21.35.12. Suppose that

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

in $D(\mathcal{O}_{\mathcal{D}'})$. 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 21.35.11.

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