Three-crossed modules

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Arvasi Z., Kuzpinari T. S., Uslu E. O.

Homology, Homotopy and Applications, vol.11, no.2, pp.161-187, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.4310/hha.2009.v11.n2.a8
  • Journal Name: Homology, Homotopy and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.161-187
  • Eskisehir Osmangazi University Affiliated: Yes


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. Copyright © 2009, International Press.