\begin{definition}[Definition:Sheaf Cohomology]
Let $X$ be a topological space.
Let $\FF$ be an abelian sheaf on $X$.
Let $\map {\mathbf {Ab} } X$ be the category of abelian sheaves on $X$.
The '''sheaf cohomology (group)''' $\map {H^i} {X, \FF}$ for $i \in \Z$, $i \ge 0$ is defined as the $i$-th right derived functor $\mathrm R^i \map \Gamma {X, -}$ of the global sections functor
:$\map \Gamma {X, -} : \map {\mathbf {Ab} } X \to \mathbf {Ab}$
applied to $\FF$.
\end{definition}