Derived functors and the homology of \(n\)-types
type: Item
instance of: scholarly article
title: Derived functors and the homology of \(n\)-types
zbMATH Open document ID: 1010.18009
DOI: 10.1016/S0021-8693(02)00048-0
author: Graham Ellis
author: M. Ladra
author: J. M. Casas
author: Teimuraz Pirashvili
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: A homotopy \(n\)-type is a connected CW-complex whose homotopy groups are trivial above dimension~\(n\). Homotopy \(n\)-types can be modelled by \(\text{ cat}^{n-1}\)-groups or, equivalently, by crossed \((n-1)\)-cubes. In this paper the authors show that the homology groups of an \(n\)-type~\(X\) can be expressed as derived functors of an abelianisation functor on crossed \((n-1)\)-cubes. They also obtain a Hopf-type formula for \(H_n(X)\).
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 18G55
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 18E25
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 1868048
zbMATH Keywords: homotopy n-type
zbMATH Keywords: \(\text{cat}^n\)-group
zbMATH Keywords: crossed n-cube
zbMATH Keywords: abelianisation
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00048-0
OpenAlex ID: W2091395363
description: scientific article; zbMATH DE number 1868048