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Zbl 1140.18012
Everaert, Tomas; Gran, Marino; van der Linden, Tim
Higher Hopf formulae for homology via Galois theory. (English)
[J] Adv. Math. 217, No. 5, 2231-2267 (2008). ISSN 0001-8708

Using Janelidze's Galois theory, the paper extends Brown-Ellis's higher Hopf formulae for homology of groups to arbitrary semi-abelian monadic categories. One has a conceptual and elementary proof (by induction on $n$ of H$_n$) viewed in a very general framework like semi-abelian categories (Janelidze, Marki, Tholen) and homological categories (Borceux, Bourn).
[Georges Hoff (Villetaneuse)]

MSC 2000:: *18G99 Homological algebra
20J99 Connections of group theory with homological algebra
55N35 Other homology theories
18E10 Exact categories, abelian categories

Keywords: semi-abelian category; Hopf formula; homology; Galois theory

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