This includes Thomason cohomology Baues cohomology, Baues-Wirsching cohomology, Andre-Quillen cohomology, Cohomology of categories, Comonadic cohomology, Cotriple homology, Monad cohomology
Generalized Andre-Quillen cohomology
Cohomology of categories Cohomology of diagrams Cohen-Macaulay cohomology Functor cohomology Generalized Tate-Vogel cohomology Gorenstein cohomology Hochschild-Mitchell cohomology
See this paper by Beligiannis and Reiten for torsion stuff
Include here stuff about operads and cohomology, including the model structures on operads and algebras.
nLab page on G10 Categorical notions of cohomology