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Statements

Subject Item
n2:RIV%2F00216224%3A14410%2F08%3A00027953%21RIV10-MSM-14410___
rdf:type
skos:Concept n17:Vysledek
dcterms: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. 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.
dcterms:title
Higher Hopf formulae for homology via Galois Theory Higher Hopf formulae for homology via Galois Theory
skos:prefLabel
Higher Hopf formulae for homology via Galois Theory Higher Hopf formulae for homology via Galois Theory
skos:notation
RIV/00216224:14410/08:00027953!RIV10-MSM-14410___
n5:aktivita
n10:P
n5:aktivity
P(LC505)
n5:cisloPeriodika
5
n5:dodaniDat
n13:2010
n5:domaciTvurceVysledku
Van der Linden, Tim
n5:druhVysledku
n11:J
n5:duvernostUdaju
n7:S
n5:entitaPredkladatele
n16:predkladatel
n5:idSjednocenehoVysledku
370102
n5:idVysledku
RIV/00216224:14410/08:00027953
n5:jazykVysledku
n14:eng
n5:klicovaSlova
Semi-abelian category; Hopf formula; Homology; Galois Theory
n5:klicoveSlovo
n6:Semi-abelian%20category n6:Homology n6:Galois%20Theory n6:Hopf%20formula
n5:kodStatuVydavatele
US - Spojené státy americké
n5:kontrolniKodProRIV
[210A45BB6123]
n5:nazevZdroje
Advances in Mathematics
n5:obor
n15:BA
n5:pocetDomacichTvurcuVysledku
1
n5:pocetTvurcuVysledku
3
n5:projekt
n8:LC505
n5:rokUplatneniVysledku
n13:2008
n5:svazekPeriodika
217
n5:tvurceVysledku
Gran, Marino Van der Linden, Tim Everaert, Thomas
n5:wos
000254098200013
s:issn
0001-8708
s:numberOfPages
37
n9:organizacniJednotka
14410