Galois theory and commutators

Everaert, Tomas;Van der Linden, Tim
(2011) Algebra Universalis — Vol. 65, n° 2, p. 161-177 (2011)

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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 Frohlich-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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Everaert, T., & Van der Linden, T. (2011). Galois theory and commutators. Algebra Universalis, 65(2), 161-177. https://doi.org/10.1007/s00012-011-0121-8 (Original work published 2011)