Remark 36.22.7. With notation as in Lemma 36.22.6. The diagram

is commutative where the top horizontal arrow is the map from the lemma, $\mu $ is the multiplication map, and $a$ comes from the adjunction map $L(g')^*Rg'_*L \to L$. The multiplication map is the adjunction map $K' \otimes _ R^\mathbf {L} R' \to K'$ for any $K' \in D(R')$.

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