Remark 59.97.1. Consider a cartesian diagram in the category of schemes:

Let $\Lambda $ be a ring and let $E \in D(X_{\acute{e}tale}, \Lambda )$ and $K \in D(Y_{\acute{e}tale}, \Lambda )$. Then there is a canonical map

For example we can define this using the canonical maps $Rf_*E \to Rc_*p^{-1}E$ and $Rg_*K \to Rc_*q^{-1}K$ and the relative cup product defined in Cohomology on Sites, Remark 21.19.7. Or you can use the adjoint to the map

which uses the adjunction maps $f^{-1}Rf_*E \to E$ and $g^{-1}Rg_*K \to K$.

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