A cubical Squier’s theorem

Abstract The homotopical Squier’s theorem relates rewriting properties of a presentation of a monoid with homotopical invariants of this monoid. This theorem has since been extended by Guiraud and Malbos, yielding a so-called polygraphic resolution of a monoid starting from a presentation with suita...

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Bibliographic Details
Published inMathematical structures in computer science Vol. 30; no. 2; pp. 159 - 172
Main Author Lucas, Maxime
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.02.2020
Subjects
Monoids
Theorems
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Summary:Abstract The homotopical Squier’s theorem relates rewriting properties of a presentation of a monoid with homotopical invariants of this monoid. This theorem has since been extended by Guiraud and Malbos, yielding a so-called polygraphic resolution of a monoid starting from a presentation with suitable rewriting properties. In this article, we argue that cubical categories are a more natural setting in which to express and possibly extend Guiraud and Malbos construction. As a proof-of-concept, we give a new proof of Squier’s homotopical theorem using cubical categories.
ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129520000018