Geodesic
Three-crossed modules
Homology, homotopy, and applications, Tome 11 (2009) no. 2, pp. 161-187.

Voir la notice de l'article provenant de la source International Press of Boston

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 cat$^3$-groups (Loday) and the 3-hypercomplexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.
DOI : 10.4310/HHA.2009.v11.n2.a8
Classification : 18D35, 18G30, 18G50, 18G55
Keywords: crossed module, 2-crossed module, simplicial group, Moore complex 
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Z. Arvasi; T. S. Kuzpinari; E. Ö. Uslu. Three-crossed modules. Homology, homotopy, and applications, Tome 11 (2009) no. 2, pp. 161-187. doi : 10.4310/HHA.2009.v11.n2.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n2.a8/

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