Definition:Acyclic Sheaf

Definition
Let $X$ be a topological space.

Let $\FF$ be an abelian sheaf on $X$.

Let $\map \Gamma {X, -} : \map {\mathbf {Ab} } X \to \mathbf {Ab}$ be the global sections functor on $X$.

Then $\FF$ is acyclic $\FF$ is $\map \Gamma {X, -}$-acyclic in the category of abelian sheaves $\map {\mathbf {Ab} } X$ on $X$.

Also see

 * Definition:Sheaf Cohomology