Remark 21.50.2. The map (21.50.0.1) is compatible with the base change map of Remark 21.19.3 in the following sense. Namely, suppose that
is a commutative diagram of ringed topoi. Let E \in D(\mathcal{O}_\mathcal {C}) and K \in D(\mathcal{O}_\mathcal {D}). Then the diagram
is commutative. Here arrows labeled t are gotten by an application of Lemma 21.18.4, arrows labeled b by an application of Remark 21.19.3, arrows labeled p by an application of (21.50.0.1), and c comes from L(g')^* \circ Lf^* = L(f')^* \circ Lg^*. We omit the verification.
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