Three Crossed Modules
Category Theory
2009-07-21 v2 Algebraic Topology
Abstract
We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 2-crossed module (Conduch\'e). We show that the category of 3-crossed modules is equivalent to the category of simplicial groups having a Moore complex of length 3. We make explicit the relationship with the cat-groups (Loday) and the 3-hyper-complexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.
Cite
@article{arxiv.0812.4685,
title = {Three Crossed Modules},
author = {Z. Arvasİ and T. S. Kuzpinari and E. Ö. Uslu},
journal= {arXiv preprint arXiv:0812.4685},
year = {2009}
}
Comments
Crossed module, 2-crossed module, Simplicial group, Moore complex