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.CSL.2021.38
URN: urn:nbn:de:0030-drops-134729
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13472/
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Tomita, Haruka

Realizability Without Symmetry

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LIPIcs-CSL-2021-38.pdf (0.5 MB)

Abstract

In categorical realizability, it is common to construct categories of assemblies and modest sets from applicative structures. In this paper, we introduce several classes of applicative structures and apply the categorical realizability construction to them. Then we obtain closed multicategories, closed categories and skew closed categories, which are more general categorical structures than Cartesian closed categories and symmetric monoidal closed categories. Moreover, we give the necessary and sufficient conditions for obtaining closed multicategories and closed categories of assemblies.

BibTeX - Entry

@InProceedings{tomita:LIPIcs:2021:13472,
  author =	{Haruka Tomita},
  title =	{{Realizability Without Symmetry}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13472},
  URN =		{urn:nbn:de:0030-drops-134729},
  doi =		{10.4230/LIPIcs.CSL.2021.38},
  annote =	{Keywords: Realizability, combinatory algebra, closed multicategory, closed category, skew closed category}
}

Keywords: Realizability, combinatory algebra, closed multicategory, closed category, skew closed category
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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