Dear Hasse,
What does the cohomology H^n(X;coefficients) classify, for X a more general object then a group and especially when X is a category? I know that the case X=group gives n-torsors.
Group cohomology also classifies crossed extensions: Huebschmann, Johannes Crossed $n$-fold extensions of groups and cohomology. Comment. Math. Helv. 55 (1980), no. 2, 302--313. There is a similar approach for cohomology of categories in: Baues, Hans-Joachim(D-MPI); Minian, Elias Gabriel(D-MPI) Track extensions of categories and cohomology. (English summary) $K$-Theory 23 (2001), no. 1, 1--13. The cases n = 0, 1, 2, 3 were known before, see references therein. Best, Fernando -- Fernando Muro Universitat de Barcelona, Departament d'Àlgebra i Geometria http://atlas.mat.ub.es/personals/muro/