The Stacks project

Lemma 6.17.5. Let $X$ be a topological space. A presheaf $\mathcal{F}$ is separated (see Definition 6.11.2) if and only if the canonical map $\mathcal{F} \to \mathcal{F}^\# $ is injective.

Proof. This is clear from the construction of $\mathcal{F}^\# $ in this section. $\square$

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