A cubical Squier's theorem

Maxime Lucas 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
Inria de Paris, CNRS - Centre National de la Recherche Scientifique, UPD7 - Université Paris Diderot - Paris 7, PPS - Preuves, Programmes et Systèmes
Abstract : The homotopical Squier's theorem relates rewriting properties of a presentation of a monoid with homotopical invariants of this monoid. Lately, this theorem has been extended, enabling one to build a so-called polygraphic resolution of a monoid starting from a presentation with suitable rewriting properties. It is currently a work in progress to get a better understanding of these results. We argue that cubical categories are a more natural setting in which to express and possibly extend those results. As a proof-of-concept, we give in this paper a new proof of Squier's homotopical theorem using cubical categories.
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https://hal.archives-ouvertes.fr/hal-01662132
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Submitted on : Tuesday, December 12, 2017 - 5:18:17 PM
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Maxime Lucas. A cubical Squier's theorem. 2017. ⟨hal-01662132⟩

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