2026-07-23T01:41:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13472 2024-03-06T10:52:10Z ddc:004 open_access

Realizability Without Symmetry Tomita, Haruka Realizability combinatory algebra closed multicategory closed category skew closed category 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Haruka Tomita 2021 Is Part Of LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2021.38 urn:nbn:de:0030-drops-134729 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.38 eng https://creativecommons.org/licenses/by/3.0/legalcode