We introduce the notion of a 3-crossed module, which extends the notions of a 1-crossed module (Whitehead) and
a 2-crossed module (Conduché). 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 cat3-groups
(Loday) and the 3-hypercomplexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.
Publié le : 2009-05-15
Classification:
Crossed module,
2-crossed module,
simplicial group,
Moore complex,
18D35,
18G30,
18G50,
18G55
@article{1296138516,
author = {Arvasi, Z. and Kuzpinari, T. S. and Uslu, E. \"O.},
title = {Three-crossed modules},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 161-187},
language = {en},
url = {http://dml.mathdoc.fr/item/1296138516}
}
Arvasi, Z.; Kuzpinari, T. S.; Uslu, E. Ö. Three-crossed modules. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 161-187. http://gdmltest.u-ga.fr/item/1296138516/