Cohomology sheaf
= Cohomology sheaf
{title2=$\mathcal H^i(E)$}
For a <cochain complex> of <sheaves> $E$, its $i$th <cohomology sheaf> is $\mathcal H^i(E)=\ker(d^i)/\operatorname{im}(d^{i-1})$, where the image and quotient are taken in <sheaves>. Its stalk at $x$ is the <cohomology> of the stalk complex, because taking stalks is exact.