Functorial factorization, well-pointedness and separability
type: Item
instance of: scholarly article
title: Functorial factorization, well-pointedness and separability
zbMATH Open document ID: 0953.18001
DOI: 10.1016/S0022-4049(98)00095-4
author: George Janelidze
author: Walter Tholen
published in: Journal of Pure and Applied Algebra
publication date: 2001-01-23T00:00:00Z
review text: Functorial factorization systems are one of the main topics in category theory. In the classical setting they are presented by two classes \({\mathcal E}\) and \({\mathcal M}\) of morphisms with appropriate closure properties that ensure a unique factorization \(f=m_f\cdot e_f\), with \(e_f\in {\mathcal E}\), \(m_f\in {\mathcal M}\), of every morphism \(f\) in the category. Weak factorization systems were introduced and studied by \textit{M. Korostenski} and \textit{W. Tholen} [J. Pure Appl. Algebra 85, No.~1, 57-72 (1993; Zbl 0778.18001)]. In the present paper the authors study the relation between weak factorization systems and well-pointed endofunctors (here well-pointedness is understood in the sense of \textit{G. M. Kelly} [Bull. Aust. Math. Soc. 22, 1-83 (1980; Zbl 0437.18004)]). The final part of the paper is dedicated to the factorization theory derived from taking separable and purely inseparable morphisms with respect to a pointed endofunctor.
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 1371460
zbMATH Keywords: weak factorization system
zbMATH Keywords: well-pointed endofunctor
zbMATH Keywords: separable morphism
zbMATH Keywords: purely inseparable morphism
zbMATH Keywords: factorization systems
reviewed by: Dikran Dikranjan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1371460