A parametricity-based formalization of semi-simplicial and semi-cubical sets - Université Paris Cité Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

A parametricity-based formalization of semi-simplicial and semi-cubical sets

Résumé

Constructions such as semi-simplicial and semi-cubical sets can be defined in the "usual way" as presheaves over respectively, the semi-simplex or semi-cube category, which we call fibered definitions, but also defined like in e.g. Voevodsky or in previous work, as a dependently-typed construction, which we call indexed. This paper describes a uniform indexed characterization of both augmented semi-simplicial and semi-cubical sets arising respectively as unary and binary iterated parametricity-based constructions. Additionally, our construction is fully formalized in Coq's dependent type theory.
Fichier principal
Vignette du fichier
paper.pdf (214.3 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY SA - Paternité - Partage selon les Conditions Initiales

Dates et versions

hal-03963929 , version 1 (02-03-2023)
hal-03963929 , version 2 (31-12-2023)

Licence

Paternité - Partage selon les Conditions Initiales

Identifiants

  • HAL Id : hal-03963929 , version 1

Citer

Hugo Herbelin, Ramkumar Ramachandra. A parametricity-based formalization of semi-simplicial and semi-cubical sets. 2023. ⟨hal-03963929v1⟩
20 Consultations
50 Téléchargements

Partager

Gmail Facebook X LinkedIn More