Lemma 18.22.4. Let (f, f^\sharp ) : (\mathop{\mathit{Sh}}\nolimits (\mathcal{C}), \mathcal{O}) \to (\mathop{\mathit{Sh}}\nolimits (\mathcal{D}), \mathcal{O}'), s : \mathcal{F} \to f^{-1}\mathcal{G} be as in Lemma 18.22.3. If f is given by a continuous functor u : \mathcal{D} \to \mathcal{C} and \mathcal{G} = h_ V^\# , \mathcal{F} = h_ U^\# and s comes from a morphism c : U \to u(V), then the commutative diagrams of Lemma 18.20.2 and Lemma 18.22.3 agree via the identifications of Lemma 18.21.3.
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