On projectivity in locally presentable categories.
type: Item
instance of: scholarly article
title: On projectivity in locally presentable categories.
zbMATH Open document ID: 1040.18008
published in: Journal of Algebra
publication date: 2004-03-14T00:00:00Z
review text: The paper is devoted to some generalizations of projectivity classes, weakly coreflexive categories and cotorsion theories from the category of \(R\)-modules to arbitrary locally presentable categories. If \(\mathcal K\) is a finitely presented category and \(\mathcal A\) is a weakly coreflexive full subcategory of \(\mathcal K\) which is closed under directed colimits in \(\mathcal K\), then \(\mathcal A\) is stably weakly coreflective. If \((\mathcal F,\mathcal C)\) is a cotorsion theory in the category \(R\)-\(mod\) such that \(\mathcal F\) is closed under directed colimits, then (\(\mathcal F\)-Mono, \(\mathcal C\)-Epi) is a stable weak factorization system.
Mathematics Subject Classification ID: 18G05
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 18C35
zbMATH DE Number: 2055649
zbMATH Keywords: projectivity class
zbMATH Keywords: weakly coreflexive category
zbMATH Keywords: cotorsion theory
zbMATH Keywords: locally presentable category
zbMATH Keywords: weak factorization system.
author: Jiří Rosický
reviewed by: Ladislav Bican
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.09.014
OpenAlex ID: W2130203920
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DOI: 10.1016/J.JALGEBRA.2003.09.014
description: scientific article; zbMATH DE number 2055649