Polygraphic resolutions and homology of monoids
type: Item
instance of: scholarly article
title: Polygraphic resolutions and homology of monoids
zbMATH Open document ID: 1169.18002
author: Yves Lafont
author: François Métayer
published in: Journal of Pure and Applied Algebra
publication date: 2009-03-30T00:00:00Z
review text: The second author [\textit{F. Métayer}, ``Resolutions by polygraphs'', Theory Appl. Categ. 11, 148--184 (2003; Zbl 1020.18001)] defined homology using resolutions of \(\omega \)-categories via computads (polygraphs). The classical homology of a monoid \(M\) is defined in terms of resolutions of \(\mathbb{Z}\) by free \(\mathbb ZM\)-modules. The first author showed that the homologies coincide in the case where \(M\) is a group while the present paper proves the coincidence for a general monoid. An unfolding construction and path \(\omega \)-category are involved.
reviewed by: Ross H. Street
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18G10
zbMATH DE Number: 5534965
zbMATH Keywords: \(n\)-category
zbMATH Keywords: computad
zbMATH Keywords: resolution
zbMATH Keywords: acyclic
zbMATH Keywords: monoid
zbMATH Keywords: rewriting system
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.10.005
OpenAlex ID: W2035377797
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DOI: 10.1016/J.JPAA.2008.10.005
description: scientific article; zbMATH DE number 5534965