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This is not an answer but an extended comment that rules out an obvious candidate for the adjunction map $\mathscr{G} \rightarrow \epsilon^!\epsilon_*(\mathscr{G})$. In the view of this, the claim about $\epsilon^!$ being the right adjoint of $\epsilon_*$ in the book seems doubtful to me, but I would be happy to be proved wrong (I would be grateful for any ...



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