Lemma 18.27.2 (0E8H)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 18: Modules on Sites
Section 18.27: Internal Hom
Lemma 18.27.2 (cite)

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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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