Sheaf cohomology assigns groups 
to a sheaf 
of Abelian groups on a topological space 
. They are the right derived
functors of the global-section functor 
(Hartshorne 1977, Stacks Project, Tag 01FT).
An injective resolution 
computes them by taking the cohomology
of the cochain complex 
. In degree zero, 
is the group of global
sections. Higher groups measure obstructions to exactness of global sections.
The same construction applies to sheaves of modules on a ringed
space and occurs in the vanishing conditions for an Ulrich
line bundle.
