Publication details

Higher Hopf formulae for homology via Galois Theory



Year of publication 2008
Type Article in Periodical
Magazine / Source Advances in Mathematics
MU Faculty or unit

Faculty of Education

Field General mathematics
Keywords Semi-abelian category; Hopf formula; Homology; Galois Theory
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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info