Relative Commutator Theory in Semi-Abelian Categories
Category Theory
2012-05-29 v1 Rings and Algebras
Abstract
Basing ourselves on the concept of double central extension from categorical Galois theory, we study a notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian category A. This commutator characterises Janelidze and Kelly's B-central extensions; when the subcategory B is determined by the abelian objects in A, it coincides with Huq's commutator; and when the category A is a variety of omega-groups, it coincides with the relative commutator introduced by the first author.
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Cite
@article{arxiv.1108.3909,
title = {Relative Commutator Theory in Semi-Abelian Categories},
author = {Tomas Everaert and Tim Van der Linden},
journal= {arXiv preprint arXiv:1108.3909},
year = {2012}
}
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22 pages