Lemma 18.11.4. Let \mathcal{C} be a site. Let \mathcal{O} \to \mathcal{O}' be an epimorphism of sheaves of rings. Let \mathcal{G}_1, \mathcal{G}_2 be \mathcal{O}'-modules. Then
\mathop{\mathrm{Hom}}\nolimits _{\mathcal{O}'}(\mathcal{G}_1, \mathcal{G}_2) = \mathop{\mathrm{Hom}}\nolimits _\mathcal {O}(\mathcal{G}_1, \mathcal{G}_2).
In other words, the restriction functor \textit{Mod}(\mathcal{O}') \to \textit{Mod}(\mathcal{O}) is fully faithful.
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