HOMOLOGY OF N-FOLD GROUPOIDS

Any semi-abelian category Aappears, via the discrete functor, as a full repletere rective subcategory of the semi-abelian category of internal groupoids in A. This allows one to study the homology of n-fold internal groupoids with coefficients in a semi-abelian category A, and to compute explicit higher Hopf formulae. The crucial concept making such computations possible is the notion of protoadditive functor, which can be seen as a natural generalisation of the notion of additive functor.