Galois theory and commutators
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2011
- DOI:
- 10.48550/arXiv.1104.0518
- arXiv:
- arXiv:1104.0518
- Bibcode:
- 2011arXiv1104.0518E
- Keywords:
-
- Mathematics - Rings and Algebras;
- Mathematics - Category Theory;
- Primary: 08C05;
- Secondary: 17D10;
- 18E10
- E-Print:
- 14 pages