Recursive data types in algebraically \(\omega\)-complete categories
type: Item
instance of: scholarly article
title: Recursive data types in algebraically \(\omega\)-complete categories
zbMATH Open document ID: 0841.18003
author: Jiří Adámek
published in: Information and Computation
publication date: 1995-07-10T00:00:00Z
review text: A connection between the notions of ``algebraically complete'' and ``algebraically compact'' category is considered. The notions were introduced by \textit{P. Freyd}. In the first case, every functor should have a least fixpoint, and in the second, a least and the largest fixpoint, that canonically coincide. It is shown that 1) several interesting categories are algebraically \(\omega\)-complete and 2) categories enriched over complete partial orders are ``almost'' \(\omega\)-compact: each localy-continuous functor has a canonical fixpoint.
Mathematics Subject Classification ID: 18B20
Mathematics Subject Classification ID: 68Q65
Mathematics Subject Classification ID: 68P05
Mathematics Subject Classification ID: 18A35
zbMATH DE Number: 767830
zbMATH Keywords: algebraically complete
zbMATH Keywords: algebraically compact
zbMATH Keywords: algebraically \(\omega\)-complete
zbMATH Keywords: least fixpoint
zbMATH Keywords: largest fixpoint
reviewed by: Serguei V. Solov'ev
MaRDI profile type: Publication
full work available at URL: inco.1995.1061
OpenAlex ID: W2055348826
DOI: 10.1006/INCO.1995.1061
description: scientific article; zbMATH DE number 767830