Lemma 6.30.7. Let $X$ be a topological space. Let $\mathcal{B}$ be a basis for the topology on $X$. Denote $\mathop{\mathit{Sh}}\nolimits (\mathcal{B})$ the category of sheaves on $\mathcal{B}$. There is an equivalence of categories

which assigns to a sheaf on $X$ its restriction to the members of $\mathcal{B}$.

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