Twisted Commutators and Internal Crossed Modules
Category Theory
2024-10-10 v1
Abstract
We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category.
Cite
@article{arxiv.2311.07489,
title = {Twisted Commutators and Internal Crossed Modules},
author = {Bo Shan Deval and Tim Van der Linden},
journal= {arXiv preprint arXiv:2311.07489},
year = {2024}
}