Three-crossed modules
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
International Press of Boston
Access Rights
info:eu-repo/semantics/openAccess
Abstract
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.
Description
Keywords
Crossed Module, 2-Crossed Module, Simplicial Group, Moore Complex
Journal or Series
Homology, Homotopy and Applications
WoS Q Value
N/A
Scopus Q Value
Q3
Volume
11
Issue
2
