Lemma 21.9.2. Let $\mathcal{C}$ be a site. Let $\mathcal{F}$ be an abelian presheaf on $\mathcal{C}$. The following are equivalent

$\mathcal{F}$ is an abelian sheaf on $\mathcal{C}$ and

for every covering $\mathcal{U} = \{ U_ i \to U\} _{i \in I}$ of the site $\mathcal{C}$ the natural map

\[ \mathcal{F}(U) \to \check{H}^0(\mathcal{U}, \mathcal{F}) \](see Sites, Section 7.10) is bijective.

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