%0 Journal Article
%T Three Crossed Modules
%A Z. Arvas£¿
%A T. S. Kuzpinari
%A E. £¿. Uslu
%J Mathematics
%D 2008
%I arXiv
%X 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$^{3}$-groups (Loday) and the 3-hyper-complexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.
%U http://arxiv.org/abs/0812.4685v2