Fundamental group functors in descent-exact homological categories

We study the notion of a fundamental group in the framework of descent-exact homological categories. This setting is sufficiently large to include several categories of “algebraic” nature such as almost abelian categories, semi-abelian categories, and categories of topological semi-abelian algebras....

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-04, Vol.310, p.64-120
Main Author: Duckerts-Antoine, Mathieu
Format: Article
Language:English
Subjects:
Galois group
Homological category
Hopf formula
Kan extension
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Summary:We study the notion of a fundamental group in the framework of descent-exact homological categories. This setting is sufficiently large to include several categories of “algebraic” nature such as almost abelian categories, semi-abelian categories, and categories of topological semi-abelian algebras. For many adjunctions in this context, we describe the fundamental groups by generalised Brown–Ellis–Hopf formulae for the integral homology of groups.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2017.02.001