Resumen de Higher Hopf formulae for homology via Galois Theory
We use Janelidze's Categorical Galois Theory to extend Brown and Ellis's higher Hopf formulae for homology of groups to arbitrary semi-abelian monadic categories. Given such a category and a chosen Birkhoff subcategory of , thus we describe the Barr�Beck derived functors of the reflector of onto in terms of centralization of higher extensions. In case is the category of all groups and is the category of all abelian groups, this yields a new proof for Brown and Ellis's formulae. We also give explicit formulae in the cases of groups vs. k-nilpotent groups, groups vs. k-solvable groups and precrossed modules vs. crossed modules.
