Higher commutator conditions for extensions in Mal'tsev categories

JOURNAL OF ALGEBRA

卷:515

Article

Duvieusart, Arnaud^1,2  Gran, Marino¹ 

[1] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2, B-1348 Louvain, Belgium

[2] Fonds Rech Sci FNRS, Brussels, Belgium

关键词: Mal'tsev categories;    Commutators;    Central extensions;    Crossed modules;    Internal groupoids;    Peiffer commutator;    Equivalence relations;    Galois theory;   

DOI  :  10.1016/j.jalgebra.2018.09.002

来源: Elsevier

【 摘 要 】

We define a Galois structure on the category of pairs of equivalence relations in an exact Mal'tsev category, and characterize central and double central extensions in terms of higher commutator conditions. These results generalize both the ones related to the abelianization functor in exact Mal'tsev categories, and the ones corresponding to the reflection from the category of internal reflexive graphs to the subcategory of internal groupoids. Some examples and applications are given in the categories of groups, precrossed modules, precrossed Lie algebras, and compact groups. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free