Three Crossed Modules

2008/12/26 by Z. Arvasi, Arvasİ, Z., T. S. Kuzpınarı +3
Mathematics · #18D35 18G30 18G50 18G55 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0812.4685

openalex publication_date 2008/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 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-hyper-complexes (Cegarra-Carrasco), which also model algebraically homotopy 4-types.

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