Lemma 20.9.2. Let $X$ be a topological space. Let $\mathcal{F}$ be an abelian presheaf on $X$. The following are equivalent

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

for every open covering $\mathcal{U} : U = \bigcup _{i \in I} U_ i$ the natural map

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

## Comments (0)

There are also: