Relative Commutator Theory in Semi-Abelian Categories

Details Relative Commutator Theory in Semi-Abelian Categories Relative Commutator Theory in Semi-Abelian Categories

2011-08-19

arxiv.org/abs/1108.3909v1

Mathematics

Category Theory

22 pages

Scientific paper

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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