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The Stacks project

Lemma 18.27.8. Let \mathcal{C} be a category, resp. a site Let \mathcal{O} \to \mathcal{O}' be a map of presheaves, resp. sheaves of rings. Then

\mathop{\mathrm{Hom}}\nolimits _\mathcal {O}(\mathcal{G}, \mathcal{F}) = \mathop{\mathrm{Hom}}\nolimits _{\mathcal{O}'}(\mathcal{G}, \mathop{\mathcal{H}\! \mathit{om}}\nolimits _\mathcal {O}(\mathcal{O}', \mathcal{F}))

for any \mathcal{O}'-module \mathcal{G} and \mathcal{O}-module \mathcal{F}.

Proof. This is the analogue of Algebra, Lemma 10.14.4. The proof is the same, and is omitted. \square


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