Relative Commutator Theory in Semi-Abelian Categories

Everaert, Tomas;Van der Linden, Tim
(2011) Journal of Pure and Applied Algebra — Vol. 216, p. 1791-1806 (2011)

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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 Beta of a semi-abelian category Alpha. This commutator characterises Janelidze and Kelly's Beta-central extensions ; when the subcategory Beta is determined by the abelian objects in Alpha, it coincides with Huq's commutator ; and when the category Alpha is a variety of Oméga-groups, it coincides with the relative commutator introduced by the first author.
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Everaert, T., & Van der Linden, T. (2011). Relative Commutator Theory in Semi-Abelian Categories. Journal of Pure and Applied Algebra, 216, 1791-1806. https://doi.org/10.1016/j.jpaa.2012.02.018 (Original work published 2011)