Lax factorization algebras
type: Item
instance of: scholarly article
title: Lax factorization algebras
zbMATH Open document ID: 1013.18001
DOI: 10.1016/S0022-4049(02)00141-X
author: Jiří Rosický
author: Walter Tholen
published in: Journal of Pure and Applied Algebra
publication date: 2002-12-02T00:00:00Z
review text: In a factorization system for a category there are two classes of morphisms each class determining the other by a diagonal fill-in condition; the fill-in morphism is required to be unique. In homotopy theory, explicitly in Quillen model categories, the same thing happens without uniqueness: weak factorization systems. As what might be considered a follow-up to the realization that factorization systems can be regarded as Eilenberg-Moore algebras for a suitable monad [see \textit{M. Korostenski} and \textit{W. Tholen}, J. Pure Appl. Algebra 85, No.~1, 57-72 (1993; Zbl 0778.18001)], this paper compares lax algebras for the monad with weak factorization systems.
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 55P05
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 18D05
zbMATH DE Number: 1839074
zbMATH Keywords: factorization system
zbMATH Keywords: Quillen model category
zbMATH Keywords: lax algebra
zbMATH Keywords: Eilenberg-Moore algebras
reviewed by: Ross H. Street
MaRDI profile type: Publication
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full work available at URL: s0022-4049(02)00141-x
OpenAlex ID: W2029919605
description: scientific article; zbMATH DE number 1839074