Higher dimensional obstruction theory in algebraic categories

AbstractIn this paper we generalize Duskin's low dimensional obstruction theory, established for the Barr-Beck's cotriple cohomogy HG2, to higher dimensions by giving a new interpretation of HGn+1 in terms of obstructions to the existence of non-singular n-extensions or realizations to n-dimensional abstract kernels. We find a surjective map Obs from the set of all n-dimensional abstract kernels with center a fixed S-module A to HGn+1(S,A) in such a way that an abstract kernel has a realization if and only if its obstruction vanishes, the set of equivalence classes of such realizations being in this case a principal homogeneous space over HGn(S,A)