A characterization of the least-fixed-point operator by dinaturality
type: Item
instance of: scholarly article
title: A characterization of the least-fixed-point operator by dinaturality
zbMATH Open document ID: 0788.18007
DOI: 10.1016/0304-3975(93)90112-7
author: Alex Simpson
published in: Theoretical Computer Science
publication date: 1993-10-17T00:00:00Z
review text: The paper addresses the question of when the least-fixed-point operator, in a Cartesian closed category of domains, is characterised as the unique dinatural transformation from the exponentiation bifunctor to the identity functor. We give a sufficient condition on a Cartesian closed full subcategory of the category of algebraic cpos for the characterisation to hold. The condition is quite mild, and the least- fixed-point operator is so characterised in many of the most commonly used categories of domains. By using retractions, the characterisation extends to the associated Cartesian closed categories of continuous cpos. However, dinaturality does not always characterise the least-fixed-point operator. We show that in Cartesian closed full subcategories of the category of continuous lattices the characterisation fails.
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 06B35
Mathematics Subject Classification ID: 68Q55
zbMATH DE Number: 417334
zbMATH Keywords: domain theory
zbMATH Keywords: fixpoint operators
zbMATH Keywords: algebraic domains
zbMATH Keywords: continuous domains
zbMATH Keywords: category of domains
zbMATH Keywords: Cartesian closed categories
zbMATH Keywords: continuous cpos
MaRDI profile type: Publication
full work available at URL: 0304-3975(93)90112-7
OpenAlex ID: W2099628768
cites work: Functorial polymorphism
cites work: Q4288818
cites work: Q3997287
cites work: Cartesian closed categories of algebraic cpos
cites work: Q4215784
cites work: Categorical fixed point semantics
cites work: The largest Cartesian closed category of domains
description: scientific article; zbMATH DE number 417334