A description of the fundamental group in terms of commutators and closure operators

A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of functors as coefficients. This makes it possible to calculate the...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2012-08, Vol.216 (8-9), p.1837-1851
Main Authors: Duckerts, Mathieu, Everaert, Tomas, Gran, Marino
Format: Article
Language:English
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Summary:A connection between the Galois-theoretic approach to semi-abelian homology and the homological closure operators is established. In particular, a generalised Hopf formula for homology is obtained, allowing the choice of a new kind of functors as coefficients. This makes it possible to calculate the fundamental groups corresponding to many interesting reflections arising, for instance, in the categories of groups, rings, compact groups and simplicial loops.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2012.02.022