Galois theory and commutators
Abstract
We prove that the relative commutator with respect to a subvariety of a variety of Omegagroups introduced by the first author can be described in terms of categorical Galois theory. This extends the known correspondence between the FroehlichLue and the JanelidzeKelly notions of central extension. As an example outside the context of Omegagroups 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 eprints
 Pub Date:
 April 2011
 arXiv:
 arXiv:1104.0518
 Bibcode:
 2011arXiv1104.0518E
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Category Theory;
 Primary: 08C05;
 Secondary: 17D10;
 18E10
 EPrint:
 14 pages