Galois theory and commutators

We prove that the relative commutator with respect to a subvariety of a variety of Omega-groups introduced by the first author can be described in terms of categorical Galois theory. This extends the known correspondence between the Froehlich-Lue and the Janelidze-Kelly notions of central extension....

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Bibliographic Details
Published in:arXiv.org 2011-04
Main Authors: Everaert, Tomas, Van der Linden, Tim
Format: Article
Language:English
Subjects:
Commutators
Online Access:Get full text
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Summary:We prove that the relative commutator with respect to a subvariety of a variety of Omega-groups introduced by the first author can be described in terms of categorical Galois theory. This extends the known correspondence between the Froehlich-Lue and the Janelidze-Kelly notions of central extension. As an example outside the context of Omega-groups we study the reflection of the category of loops to the category of groups where we obtain an interpretation of the associator as a relative commutator.
ISSN:2331-8422
DOI:10.48550/arxiv.1104.0518