Cartesian closedness in categories of relational systems
type: Item
instance of: scholarly article
title: Cartesian closedness in categories of relational systems
zbMATH Open document ID: 0677.18007
DOI: 10.1007/BF01237574
author: Josef Šlapal
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: Two notions, called reflexivity and diagonality, for relational systems (considered as sets of maps from an index set I to some set X) are defined. A system is reflexive if it contains all constant maps. It is diagonal if (for \(I\neq \emptyset)\) the existence of two families of maps \(\{r_ i| i\in I\}\) and \(\{s_ j| j\in I\}\) such that \(s_ i(j)=r_ j(i)\) implies that the map \(t(i)=r_ i(i)\) (i\(\in I)\) belongs to the system. Let \(REL_ I\) be the full subcategory of the category of relational systems with index set I whose objects are reflexive and diagonal relational systems. The main theorem says that \(REL_ I\) is cartesian closed for every set I. Some examples are considered.
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 18B10
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 4108980
zbMATH Keywords: cartesian closed category
zbMATH Keywords: category of relational systems
reviewed by: Serguei V. Solov'ev
MaRDI profile type: Publication
cites work: Q5586461
cites work: Q4079792
cites work: On a power of relational structures
cites work: A Cartesian closed topological category of sequential spaces
description: scientific article; zbMATH DE number 4108980