Higher-dimensional normalisation strategies for acyclicity
type: Item
instance of: scholarly article
title: Higher-dimensional normalisation strategies for acyclicity
zbMATH Open document ID: 1266.18008
author: Yves Guiraud
author: Philippe Malbos
published in: Advances in Mathematics
publication date: 2012-10-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.0558
reviewed by: Yu Li
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 68Q42
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 18G20
zbMATH DE Number: 6094113
zbMATH Keywords: rewriting
zbMATH Keywords: polygraphic resolution
zbMATH Keywords: homology of small categories
MaRDI profile type: Publication
OpenAlex ID: W2092347581
arXiv ID: 1011.0558
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DOI: 10.1016/J.AIM.2012.05.010
review text: In 1994, Squier linked the existence of a finite convergent presentation of a monoid to a homotopical invariant of monoids, called finite derivation type. Using this result, he gave another proof that there exists finitely generated monoids with a decidable word problem that do no admit a finite convergent presentation.NEWLINENEWLINE In this paper, the authors use normalisation strategies to construct an explicit polygraphic resolution from a convergent presentation. They define a higher-dimensional homotopical finiteness condition for higher categories which is an extension of Squier's finite derivation type for monoids, and relate it to a new homological finiteness condition.
description: scientific article; zbMATH DE number 6094113