Higher Hopf formulae for homology via Galois Theory

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14410%2F08%3A00027953" target="_blank" >RIV/00216224:14410/08:00027953 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Higher Hopf formulae for homology via Galois Theory
Original language 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.
Czech name
Vyšší Hopfovy formule pro homologie pomocí Galoisovy teorie
Czech description
Pomocí Janelidzeovy kategoriální Galoisovy teorie rozšiřujeme Brownovu a Ellisovu vyšší Hopfovu formuli pro homologie grup.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/LC505" target="_blank" >LC505: Eduard Čech Center for Algebra and Geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)