Nominal Presentations of the Cubical Sets Model of Type Theory
نویسنده
چکیده
The cubical sets model of Homotopy Type Theory was introduced by Bezem, Coquand and Huber using a particular category of presheaves. We show that this category is equivalent to a category of sets whose elements have a finite support property with respect to an action of a monoid of name substitutions; and that this is isomorphic to a category of nominal sets equipped with source and target maps. This formulation of cubical sets brings out the connection between paths and the nominal sets notion of name abstraction. We organize it as a category with families, suitable for modelling Type Theory. This formulation in terms of actions of monoids of name substitutions also encompasses a variant category of cubical sets, namely ones with diagonals, that corresponds to Grothendieck’s “smallest test category”. 1998 ACM Subject Classification F.4.1 Mathematical Logic; D.3.3 Language Constructs and Features
منابع مشابه
An Equivalent Presentation of the Bezem-Coquand-Huber Category of Cubical Sets
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