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arXiv · 1104.0518

Galois theory and commutators

Tomas Everaert·Tim Van der Linden
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Abstract

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.

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Tomas Everaert, Tim Van der Linden. 2011-04-04. Galois theory and commutators. https://doi.org/10.1007/s00012-011-0121-8

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