Localizations of algebraic categories
type: Item
instance of: scholarly article
title: Localizations of algebraic categories
zbMATH Open document ID: 0854.18007
DOI: 10.1016/0022-4049(95)00076-3
published in: Journal of Pure and Applied Algebra
publication date: 1997-01-22T00:00:00Z
review text: The main result of the paper characterizes the localizations of concrete algebraic categories (= categories of Eilenberg-Moore algebras for a monad over \({\mathcal S}et\)) as the exact categories which have a regular generator admitting all copowers. It was known previously that the additional requirement of the regular generator being regular projective characterizes the concrete algebraic categories themselves, and that there also exists an easy characterization of the regular-epireflective subcategories and of all subcategories of concrete algebraic categories in this context. In proving his main result, the author makes essential use of the exact completion theory as presented in his work with \textit{A. Carboni} [``Regular and exact completions'', ibid. (to appear)].
reviewed by: Walter Tholen
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 18E35
Mathematics Subject Classification ID: 18C15
zbMATH DE Number: 897495
zbMATH Keywords: Eilenberg-Moore category
zbMATH Keywords: exact category
zbMATH Keywords: Kleisli category
zbMATH Keywords: localizations
zbMATH Keywords: algebraic categories
zbMATH Keywords: Eilenberg-Moore algebras
zbMATH Keywords: regular generator
zbMATH Keywords: regular-epireflective subcategories
zbMATH Keywords: exact completions
author: E. M. Vitale
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00076-3
OpenAlex ID: W4210487587
cites work: Q4856547
cites work: Regular and exact completions
cites work: Q4124986
cites work: Q4896532
cites work: Q4322441
description: scientific article; zbMATH DE number 897495