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    Three-crossed modules
    (International Press of Boston, 2009) Arvasi, Zekeriya; Kuzpınarı, Tufan Sait; Uslu, Enver Önder
    We introduce the notion of a 3-crossed module, which extends the notions of a 1-crossed module (Whitehead) and a 2-crossed module (Conduche). 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.