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.
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Licence : CC BY SA - Paternité - Partage selon les Conditions Initiales
Licence : CC BY SA - Paternité - Partage selon les Conditions Initiales