Lemma 18.27.2. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{F}, \mathcal{G}$ be sheaves of $\mathcal{O}$-modules. Then formation of $\mathop{\mathcal{H}\! \mathit{om}}\nolimits _\mathcal {O}(\mathcal{F}, \mathcal{G})$ commutes with restriction to $U$ for $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$.

**Proof.**
Immediate from the definition.
$\square$

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