Dialogue categories and chiralities
type: Item
instance of: scholarly article
title: Dialogue categories and chiralities
zbMATH Open document ID: 1402.18008
DOI: 10.4171/PRIMS/185
author: Paul-André Melliès
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2016-12-30T00:00:00Z
review text: Summary: In this paper, we consider a two-sided notion of dialogue category which we call dialogue chirality and which we formulate as an adjunction between a monoidal category \(\mathcal{A}\) of proofs and a monoidal category \(\mathcal{B}\) of counter-proofs equivalent to its opposite category \(\mathcal{A}^{\mathrm{op}(0,1)}\). The two-sided formulation of dialogue categories is compared to the original one-sided formulation by exhibiting a 2-dimensional equivalence between a 2-category of dialogue categories and a 2-category of dialogue chiralities. The resulting coherence theorem clari es in what sense every dialogue chirality may be stricti ed to an equivalent dialogue category.
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 18D50
Mathematics Subject Classification ID: 03F52
zbMATH DE Number: 6669846
zbMATH Keywords: categories and chiralities
zbMATH Keywords: Cartesian closed categories and chiralities
zbMATH Keywords: dialogue categories and chiralities
zbMATH Keywords: classical logic
zbMATH Keywords: linear logic
zbMATH Keywords: tensorial logic
zbMATH Keywords: game semantics
zbMATH Keywords: logical polarities
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/prims/185
OpenAlex ID: W2558471714
description: scientific article; zbMATH DE number 6669846