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A cubical Squier’s theorem

Published online by Cambridge University Press:  06 February 2020

Maxime Lucas Open the ORCID record for Maxime Lucas [Opens in a new window]
Maxime Lucas*
Affiliation:
Inria, LS2N, Université de Nantes, France
*
Email: [email protected]
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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.

Keywords

Cubical categoriescoherencerewriting
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 2 , February 2020 , pp. 159 - 172
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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