3-types of simplicial groups and braided regular crossed modules
type: Item
instance of: scholarly article
title: 3-types of simplicial groups and braided regular crossed modules
zbMATH Open document ID: 1113.18006
published in: Homology, Homotopy and Applications
publication date: 2007-01-15T00:00:00Z
full work available at URL: a5
review text: There are various algebraic models of homotopy 3-types. The authors introduce a new model: the braided regular crossed modules. They connect this to other models as follows: (i) they construct a category equivalence between the category of braided regular crossed modules and the category of simplical groups with Moore complex of length 2; (ii) they explicitly calculate a category equivalence between the category of braided regular crossed modules and the category of crossed squares; (iii) they explicitly construct a quadratic module from any braided crossed module in a functorial way. The last two items are just applications of the first one. The notions above are too involved to define here. Nevertheless, the authors recall the definition of all the models and functors they use. Their constructions are explicit and their proofs are lengthy verifications of all the requirements of the various definitions.
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 5116064
zbMATH Keywords: braided regular crossed modules
zbMATH Keywords: algebraic models of homotopy 3-types
zbMATH Keywords: simplical groups
zbMATH Keywords: 2-crossed modules
author: Zekeriya Arvasi
author: Erdal Ulualan
MaRDI profile type: Publication
DOI: 10.4310/HHA.2007.V9.N1.A5
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description: scientific article; zbMATH DE number 5116064