The concept of a binary relation over partial enumerated sets
type: Item
instance of: scholarly article
title: The concept of a binary relation over partial enumerated sets
zbMATH Open document ID: 0795.03061
DOI: 10.1007/BF02259948
author: A. Orlicki
published in: Algebra and Logic
publication date: 1994-04-12T00:00:00Z
full work available at URL: https://eudml.org/doc/187612
review text: Binary relations over total enumerated sets have been introduced and investigated in an earlier paper [the author, Z. Math. Logik Grundlagen Math. 34, No. 3, 265-276 (1988; Zbl 0657.03026)]. In the present paper we analyze the possibility of extending this concept of partial enumerated sets. In doing so, we work within the general methodological framework outlined in the introduction to the above-mentioned paper. In the first section, we consider some class of monads called ``lifts of the power set monad''. The monads serve as tools for describing the relations investigated here. In the second section, we discuss possible natural definitions of relations over partial enumerated sets. Together with relations described by Kleisli categories of suitable monads (called ``\(T\)-relations''), we also introduce the so-called ``quasi-relations''. The latter class cannot be described by ``monadic machinery''.
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 18B99
zbMATH DE Number: 536665
zbMATH Keywords: binary relation
zbMATH Keywords: lifts of the power set monad
zbMATH Keywords: quasi-relations
zbMATH Keywords: partial enumerated sets
zbMATH Keywords: Kleisli categories
MaRDI profile type: Publication
cites work: Binary Relations Over the Category of Enumerated Sets
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cites work: Q5573961
cites work: A representation of the category of algebras over different monads by the category of algebras over one suitable monad in a category of pointed monads
OpenAlex ID: W2066800955
description: scientific article; zbMATH DE number 536665