How accessible are categories of algebras?
type: Item
instance of: scholarly article
title: How accessible are categories of algebras?
zbMATH Open document ID: 1023.18001
DOI: 10.1016/S0022-4049(02)00328-6
author: Jiří Adámek
author: Lurdes Sousa
published in: Journal of Pure and Applied Algebra
publication date: 2003-06-18T00:00:00Z
review text: The aim of the paper is to study properties of the category \({\mathcal A}lg F\) of \(F\)-algebras for a given endofunctor \(F:{\mathcal A}\to{\mathcal A}\). More precisely, let \(\lambda\) be a regular cardinal and \(\lambda^+\) its successor. An endofunctor \(F:{\mathcal A}\to{\mathcal A}\) is called \(\lambda\)-accessible (resp. strongly \(\lambda\)-accessible) provided that the category \({\mathcal A}\) is \(\lambda\)-accessible and \(F\) preserves \(\lambda\)-filtered colimits (resp. and \(\lambda\)-presentable objects). The following results are proved: if \({\mathcal A}\) is locally \(\lambda\)-multipresentable and \(F\) is \(\lambda\)-accessible, then \({\mathcal A}lg F\) is locally \(\lambda\)-multipresentable; if \(F\) is strongly \(\lambda\)-accessible, then \({\mathcal A}lg F\) is \(\lambda^+\)-accessible. Several examples and counterexamples are given.
Mathematics Subject Classification ID: 18A05
Mathematics Subject Classification ID: 18D99
Mathematics Subject Classification ID: 18A22
zbMATH DE Number: 1930188
zbMATH Keywords: algebra for endofunctor
zbMATH Keywords: accessible category
zbMATH Keywords: accessible functor
zbMATH Keywords: regular cardinal
reviewed by: Yves Diers
MaRDI profile type: Publication
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full work available at URL: s0022-4049(02)00328-6
OpenAlex ID: W2107846795
description: scientific article; zbMATH DE number 1930188