Lemma 21.20.1. Let $f : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}')$ be a morphism of ringed topoi. The functor $Rf_*$ defined above and the functor $Lf^*$ defined in Lemma 21.19.2 are adjoint:

bifunctorially in $\mathcal{F}^\bullet \in \mathop{\mathrm{Ob}}\nolimits (D(\mathcal{O}))$ and $\mathcal{G}^\bullet \in \mathop{\mathrm{Ob}}\nolimits (D(\mathcal{O}'))$.

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