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Preprints, Working Papers, ... Year : 2023

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

Abstract

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.
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Dates and versions

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

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  • HAL Id : hal-03963929 , version 2

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Hugo Herbelin, Ramkumar Ramachandra. A parametricity-based formalization of semi-simplicial and semi-cubical sets. 2023. ⟨hal-03963929v2⟩
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