Lemma 21.19.1. 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 21.18.2 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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