Lemma 18.21.4. Let (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}) be a ringed topos. If s : \mathcal{G} \to \mathcal{F} is a morphism of sheaves on \mathcal{C} then there exists a natural commutative diagram of morphisms of ringed topoi
where (j, j^\sharp ) is the localization morphism of the ringed topos (\mathop{\mathit{Sh}}\nolimits (\mathcal{C})/\mathcal{F}, \mathcal{O}_\mathcal {F}) at the object \mathcal{G}/\mathcal{F}.
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