Group-groupoid actions and liftings of crossed modules
Category Theory
2018-08-17 v1 Algebraic Topology
Abstract
The aim of this paper is to define the notion of lifting of a crossed module via a group morphism and give some properties of this type of the lifting. Further we obtain a criterion for a crossed module to have a lifting of crossed module. We also prove that the liftings of a certain crossed module constitute a category; and that this category is equivalent to the category of covers of that crossed module and hence to the category of group-groupoid actions of the corresponding groupoid to that crossed module.
Keywords
Cite
@article{arxiv.1601.07096,
title = {Group-groupoid actions and liftings of crossed modules},
author = {Osman Mucuk and Tunçar Şahan},
journal= {arXiv preprint arXiv:1601.07096},
year = {2018}
}
Comments
18 pages, research paper, LaTeX2e, xypic