Fundamental groups in E-semi-abelian categories
(2013)
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FundamentalgroupsinE-semi-abeliancategories.pdf
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- Authors
- Supervisors
- Gran, Marino
- Abstract
- The main aim of this thesis is to begin the study of the notion of fundamental group, coming from the categorical Galois theory, in the framework of E-semi-abelian categories. This new context is sufficiently wide to include several categories of « algebraic » nature such as the semi-abelian categories, the integral almost abelian categories and the categories of topological semi-abelian algebras. At the abstract level, the fundamental groups are described by generalisations of the Brown-Ellis-Hopf formulae for the integral homology of groups, where the homological closure operators naturally occur. As an application, we give various descriptions of the fundamental groups corresponding to many adjunctions in the categories of groups, rings, topological groups and compact groups. This thesis yet provides another approach to the homology of non-abelian structures.
- Affiliations
Citations
Duckerts-Antoine, M. (2013). Fundamental groups in E-semi-abelian categories. https://hdl.handle.net/2078.5/26815