License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2018.7
URN: urn:nbn:de:0030-drops-114118
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11411/
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Uemura, Taichi

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

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LIPIcs-TYPES-2018-7.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{uemura:LIPIcs:2019:11411,
  author =	{Taichi Uemura},
  title =	{{Cubical Assemblies, a Univalent and Impredicative Universe and a Failure of Propositional Resizing}},
  booktitle =	{24th International Conference on Types for Proofs and Programs (TYPES 2018)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-106-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{130},
  editor =	{Peter Dybjer and Jos{\'e} Esp{\'\i}rito Santo and Lu{\'\i}s Pinto},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11411},
  URN =		{urn:nbn:de:0030-drops-114118},
  doi =		{10.4230/LIPIcs.TYPES.2018.7},
  annote =	{Keywords: Cubical type theory, Realizability, Impredicative universe, Univalence, Propositional resizing}
}

Keywords: Cubical type theory, Realizability, Impredicative universe, Univalence, Propositional resizing
Collection: 24th International Conference on Types for Proofs and Programs (TYPES 2018)
Issue Date: 2019
Date of publication: 18.11.2019

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