De Rham–Weil theorem
In algebraic topology, the De Rham–Weil theorem allows computation of sheaf cohomology using an acyclic resolution of the sheaf in question. Let   be a sheaf on a topological space  and   a resolution of   by acyclic sheaves. Then   

where   denotes the -th sheaf cohomology group of  with coefficients in   

The De Rham–Weil theorem follows from the more general fact that derived functors may be computed using acyclic resolutions instead of simply injective resolutions. References 

Homological algebra
Sheaf theory