Categories of relations and functional relations
type: Item
instance of: scholarly article
title: Categories of relations and functional relations
zbMATH Open document ID: 0981.18002
DOI: 10.1023/A:1008651524610
author: Romaine Jayewardene
author: Oswald Wyler
published in: Applied Categorical Structures
publication date: 2002-03-21T00:00:00Z
review text: In this nice article the authors consider relations and their composition in a category having finite limits with \(({\mathcal E},{\mathcal M})\)-factorization structure, where \({\mathcal M}\) consists of monomorphisms but \({\mathcal E}\) is not restricted to epimorphisms [\textit{P. J. Freyd} and \textit{G. M. Kelly}, J. Pure Appl. Algebra 2, 169-191 (1972; Zbl 0257.18005)]. An associativity criterion for composition of relations is achieved [see also, \textit{A. Klein}, Ill. J. Math. 14, 536-550 (1970; Zbl 0217.07001)] and the categories of functional and induced relations are studied. It is shown that under certain assumptions, the categories of relations on functional and induced relations are isomorphic to the category of relations for the given category. Finally, an illuminating example based on the categories of fuzzy sets are taken into account. In this example functional relations are focused for genuine reason [\textit{D. Ponasse}, Fuzzy Sets Syst. 28, No. 3, 235-244 (1988; Zbl 0675.03032)].
reviewed by: T. M. G. Ahsanullah
Mathematics Subject Classification ID: 18B10
Mathematics Subject Classification ID: 18A32
zbMATH DE Number: 1563348
zbMATH Keywords: composition of relations
zbMATH Keywords: induced relations
zbMATH Keywords: functional relations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563348