Varieties of simplicial groupoids. I: Crossed complexes
type: Item
instance of: scholarly article
title: Varieties of simplicial groupoids. I: Crossed complexes
zbMATH Open document ID: 0888.55005
DOI: 10.1016/S0022-4049(96)00038-2
published in: Journal of Pure and Applied Algebra
publication date: 1998-06-03T00:00:00Z
review text: The paper is a contribution to the theory of algebraic models for homotopy types. \textit{W. G. Dwyer} and \textit{D. M. Kan} [Indag. Math. 46, 379-385 (1984; Zbl 0559.55023)] have shown that simplicial groupoids model all homotopy types completely. Partial models include crossed complexes which have been extensively studied by \textit{R. Brown} and \textit{P. J. Higgins} [J. Pure Appl. Algebra 47, 1-33 (1987; Zbl 0621.55009)]. In the paper, the simplicial groupoids that correspond to crossed complexes are shown to form a variety (epi-reflective subcategory) within the category of all simplicial groupoids and the corresponding verbal subgroupoid is identified.
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55U35
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 18G55
zbMATH DE Number: 1076655
zbMATH Keywords: simplicial groupoid
zbMATH Keywords: crossed complex
zbMATH Keywords: variety
zbMATH Keywords: verbal subgroupoid
zbMATH Keywords: homotopy type
zbMATH Keywords: groupoid \(T\)-complex
zbMATH Keywords: Dold-Kan theorem
author: Philip John Ehlers
author: Timothy Porter
reviewed by: Klaus Heiner Kamps
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1076655