A homotopy 2-groupoid from a fibration
type: Item
instance of: scholarly article
title: A homotopy 2-groupoid from a fibration
zbMATH Open document ID: 0914.55006
author: Klaus Heiner Kamps
author: Timothy Porter
published in: Homology, Homotopy and Applications
publication date: 1999-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/232947
full work available at URL: volume1-1.htm
review text: It is well known that the homotopy exact sequence of a based fibration with total space \(E\) and fibre \(F\) contains a crossed module \(\pi_1(F)\to\pi_1(E)\); since a crossed module is equivalent to a \(\text{cat}^1\)-group, a based fibration therefore yields a \(\text{cat}^1\)-group. For a non-based fibration, the authors analogously construct a \(2\)-groupoid; they also show that this is equivalent to a \(\text{cat}^1\)-groupoid.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 55R05
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 20L05
Mathematics Subject Classification ID: 55Q05
zbMATH DE Number: 1285144
zbMATH Keywords: \(2\)-groupoid
zbMATH Keywords: \(\text{cat}^1\)-groupoid
zbMATH Keywords: crossed module
zbMATH Keywords: fibration
MaRDI profile type: Publication
OpenAlex ID: W1973368144
DOI: 10.4310/HHA.1999.V1.N1.A2
description: scientific article; zbMATH DE number 1285144