License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2023.5
URN: urn:nbn:de:0030-drops-179897
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17989/
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Uemura, Taichi

Homotopy Type Theory as Internal Languages of Diagrams of ∞-Logoses

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LIPIcs-FSCD-2023-5.pdf (0.9 MB)

Abstract

We show that certain diagrams of ∞-logoses are reconstructed in internal languages of their oplax limits via lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single ∞-logos but also a diagram of ∞-logoses. This also provides a higher dimensional version of Sterling’s synthetic Tait computability - a type theory for higher dimensional logical relations.

BibTeX - Entry

@InProceedings{uemura:LIPIcs.FSCD.2023.5,
  author =	{Uemura, Taichi},
  title =	{{Homotopy Type Theory as Internal Languages of Diagrams of ∞-Logoses}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17989},
  URN =		{urn:nbn:de:0030-drops-179897},
  doi =		{10.4230/LIPIcs.FSCD.2023.5},
  annote =	{Keywords: Homotopy type theory, ∞-logos, ∞-topos, oplax limit, Artin gluing, modality, synthetic Tait computability, logical relation}
}

Keywords: Homotopy type theory, ∞-logos, ∞-topos, oplax limit, Artin gluing, modality, synthetic Tait computability, logical relation
Collection: 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Issue Date: 2023
Date of publication: 28.06.2023

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