Salvato in:
Dettagli Bibliografici
Autori principali: Herbelin, Hugo, Ramachandra, Ramkumar
Natura: Preprint
Pubblicazione: 2023
Soggetti:
Accesso online:https://arxiv.org/abs/2401.00512
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Sommario:
  • Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of n-simplices or n-cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call indexed. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively in its unary and binary variants. We exploit this correspondence to develop an original uniform indexed definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.