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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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