Classification of abelian track categories
type: Item
instance of: scholarly article
title: Classification of abelian track categories
zbMATH Open document ID: 0998.18002
DOI: 10.1023/A:1015607114629
author: Hans-Joachim Baues
author: M. Jibladze
published in: \(K\)-Theory
publication date: 2002-08-21T00:00:00Z
review text: A groupoid is said to be abelian if the automorphism group of each object is abelian. A track category is a 2-category where 2-cells form a groupoid. The paper shows that any abelian track category has canonically a structure of linear track extension. This structure was defined in order to describe the 3-cohomology of categories with abelian and functorial coefficients. A track category is then determined, up to weak equivalence, by a characteristic cohomology class: the universal Toda bracket.
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18E10
zbMATH DE Number: 1786895
zbMATH Keywords: abelian groupoid
zbMATH Keywords: extension of categories
zbMATH Keywords: 2-category
zbMATH Keywords: linear track extension
zbMATH Keywords: 3-cohomology of categories
zbMATH Keywords: universal Toda bracket
reviewed by: Georges Hoff
MaRDI profile type: Publication
full work available at URL: a:1015607114629
OpenAlex ID: W1990861361
description: scientific article; zbMATH DE number 1786895