I am learning some sheaf theory and sheaf cohomology from the book by Torsten Wedhorn.
Sheaves seem to be quite a flexible tool, since one can have sheaves of rings, sheaves of abelian groups and so on.
My question is: are there some important results in sheaf theory , given how flexible they appear to be as a tool ? or are the results specialised to particular types of sheaves over particular types of topological spaces ?