Relative commutator theory in semi-abelian categories
نویسندگان
چکیده
Based 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 subcategoryB is determined by the abelian objects inA, it coincides with Huq’s commutator; and when the category A is a variety of Ω-groups, it coincides with the relative commutator introduced by the first author. © 2012 Elsevier B.V. All rights reserved.
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