Relative Commutator Theory in Semi-Abelian Categories

Tomas Everaert; Tim Van der Linden

doi:10.1016/j.jpaa.2012.02.018

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arXiv · 1108.3909

Relative Commutator Theory in Semi-Abelian Categories

Tomas Everaert·Tim Van der Linden

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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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Tomas Everaert, Tim Van der Linden. 2011-08-19. Relative Commutator Theory in Semi-Abelian Categories. https://doi.org/10.1016/j.jpaa.2012.02.018

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