The Category of Crossed Modules of Crossed Modules and Its Associated Double Groupoids
Category Theory
2018-02-06 v1
Abstract
In this work we study the notion of Whitehead sequence in the category of crossed modules and actions of crossed modules. As expected, Whitehead sequences in that context are the same as crossed squares. We investigate under which conditions a Whitehead sequence of crossed modules gives rise to an internal groupoid in the category of crossed modules. In other words, we explicitly investigate the so called "Smith is Huq" condition in the category of crossed modules.
Keywords
Cite
@article{arxiv.1802.01204,
title = {The Category of Crossed Modules of Crossed Modules and Its Associated Double Groupoids},
author = {Nelson Martins-Ferreira and Ahmet Emin Tatar},
journal= {arXiv preprint arXiv:1802.01204},
year = {2018}
}
Comments
14 pages