Regular relations and bicartesian squares
type: Item
instance of: scholarly article
title: Regular relations and bicartesian squares
zbMATH Open document ID: 0802.18004
DOI: 10.1016/0304-3975(94)90086-8
published in: Theoretical Computer Science
publication date: 1994-12-19T00:00:00Z
review text: A relation \(R\) is regular iff \(R=R*\widehat R*R\), where \(*\) indicates the relational composition and \(\widehat{R}\) is the inverse of \(R\). Regular relations arise in many areas of computer science and are characterized in a number of ways. The purpose of the paper is to recast the properties of regular relations in categorical terms. The result is that regular relations correspond to unique bicartesian squares in Set, where a bicartesian square in a category is a commutative square that is both a pushout and a pullback.
Mathematics Subject Classification ID: 18B10
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 68Q65
zbMATH DE Number: 612376
zbMATH Keywords: regular relations
zbMATH Keywords: bicartesian squares
zbMATH Keywords: programming theory
author: Richard Banach
reviewed by: Andrea Maggiolo-Schettini
MaRDI profile type: Publication
full work available at URL: 0304-3975(94)90086-8
OpenAlex ID: W2069707918
cites work: Q4693062
cites work: Locating the contractum in the double pushout approach
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cites work: Regularity of relations: A measure of uniformity
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cites work: Q5287518
cites work: Q5686039
description: scientific article; zbMATH DE number 612376