On quasivarieties and varieties as categories
type: Item
instance of: scholarly article
title: On quasivarieties and varieties as categories
zbMATH Open document ID: 1072.08001
author: Jiří Adámek
published in: Studia Logica
publication date: 2005-04-07T00:00:00Z
review text: The paper deals with a classical topic of category theory because the first characterizations of varieties and quasivarieties of universal algebras were found by F. W. Lawvere and J. R. Isbell in the early 1960s. The author weakens their assumptions with the aim to get ``optimum'' characterizations. The motivating idea is to combine cocompleteness with a suitable notion of a generator. The paper is written in a way accessible both to a category theorist and to a universal algebraist.
reviewed by: Jiří Rosický
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 18A35
Mathematics Subject Classification ID: 08-02
Mathematics Subject Classification ID: 18-02
zbMATH DE Number: 2153434
zbMATH Keywords: variety
zbMATH Keywords: quasivariety
zbMATH Keywords: category of algebras
zbMATH Keywords: regular generator
zbMATH Keywords: exact generator
zbMATH Keywords: pseudoequivalence
zbMATH Keywords: cocompleteness
MaRDI profile type: Publication
full work available at URL: s11225-005-7033-6
OpenAlex ID: W89224262
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DOI: 10.1007/S11225-005-7033-6
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description: scientific article; zbMATH DE number 2153434