Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Hopf formulae for homology via Galois Theory   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.

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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin