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Abstract
We use Janelidze's Categorical Galois Theory to extend Brown and Ellis's higher Hopf formulae for homology of groups to arbitrary semiabelian monadic categories. Given such a category A and a chosen Birkhoff subcategory B of A, thus we describe the BarrBeck derived functors of the reflector of A onto B in terms of centralization of higher extensions. In case A is the category Gp of all groups and B is the category Ab 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. knilpotent groups, groups vs. ksolvable groups and precrossed modules vs. crossed modules.
Original language  English 

Pages (fromto)  22312267 
Number of pages  37 
Journal  Advances in Mathematics 
Volume  217 
Issue number  5 
Publication status  Published  2008 
Keywords
 semiabelian category
 Hopf formula
 Galois theory
 homology
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Tomas Everaert (Member)
1 May 2006 → 1 Feb 2007Activity: Membership › Membership of external research organisation