I have recently became familiar with the theory of Grothendieck Topologies and Cech cohomology for sheaves over a site. It seems that many of homological concepts in algebra, can be formulated in terms of cohomology of an appropriate sheaf on a site, for example $\mathrm{Ext}^1(X,Y)$ is related to some kind of torsors and then to first Cech cohomology.
I wonder if there is a reference which developed cohomology theories as a special case of cohomology of sheaves over sites? Thanks!