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Cubical Assemblies, a Univalent and Impredicative Universe and a Failure of Propositional Resizing

Author Taichi Uemura

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Author Details

Taichi Uemura
  • University of Amsterdam, Amsterdam, The Netherlands

Funding

This work is part of the research programme "The Computational Content of Homotopy Type Theory" with project number 613.001.602, which is financed by the Netherlands Organisation for Scientific Research (NWO).

Acknowledgements

I would like to thank Benno van den Berg, Martijn den Besten and Andrew Swan for helpful discussions and comments, and Bas Spitters, Steve Awodey and the anonymous reviewer for their comments, questions and suggestions.

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Taichi Uemura. Cubical Assemblies, a Univalent and Impredicative Universe and a Failure of Propositional Resizing. In 24th International Conference on Types for Proofs and Programs (TYPES 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 130, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.TYPES.2018.7

Abstract

We construct a model of cubical type theory with a univalent and impredicative universe in a category of cubical assemblies. We show that this impredicative universe in the cubical assembly model does not satisfy a form of propositional resizing.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Theory of computation → Denotational semantics
Keywords
  • Cubical type theory
  • Realizability
  • Impredicative universe
  • Univalence
  • Propositional resizing

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