Higher Hopf formulae for homology via Galois Theory
| dc.creator | Everaert, Tomas | |
| dc.creator | Gran, Marino | |
| dc.creator | Van der Linden, Tim | |
| dc.date | 2007-01-29 | |
| dc.date | 2007-05-21 | |
| dc.date.accessioned | 2026-07-07T09:56:55Z | |
| dc.date.available | 2026-07-07T09:56:55Z | |
| dc.description | 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 A and a chosen Birkhoff subcategory B of A, thus we describe the Barr-Beck 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. k-nilpotent groups, groups vs. k-solvable groups and precrossed modules vs. crossed modules. | |
| dc.description | 35 pages; major changes in section 5, minor changes elsewhere | |
| dc.identifier | https://arxiv.org/abs/math/0701815 | |
| dc.identifier | http://arxiv.org/abs/math/0701815 | |
| dc.identifier | Advances in Mathematics 217 (2008) 2231-2267 | |
| dc.identifier | doi:10.1016/j.aim.2007.11.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167156 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Category Theory | |
| dc.subject | 18G, 20J, 55N35, 18E10 | |
| dc.title | Higher Hopf formulae for homology via Galois Theory | |
| dc.type | text |