Effective codescent morphisms, amalgamations and factorization systems
type: Item
instance of: scholarly article
title: Effective codescent morphisms, amalgamations and factorization systems
zbMATH Open document ID: 1127.18002
author: Dali Zangurashvili
published in: Journal of Pure and Applied Algebra
publication date: 2007-02-12T00:00:00Z
review text: Let \({\mathcal C}\) be a category with pullbacks and with a factorization system \((\mathcal E,\mathcal M)\) where all morphisms in \(\mathcal M\) are monos. The main result of the paper gives a necessary and sufficient condition on a descent morphism in \({\mathcal C}\) to be effective, involving descent data of a special kind only. This theorem is then used to obtain conditions on a functor \({\mathcal C}\to{\mathcal X}\) between categories with pullbacks in order that the property of every descent morphism being effective lifts from \({\mathcal X}\) to \({\mathcal C}\). In consequence of the first result, every regular monomorphism in the category of topological spaces is an effective codescent morphism, and then the second theorem carries over this property to a number of other categories of a `topological nature'. Beside factorization systems, the notion dual to the amalgamation property also plays a key role in these investigations.
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 46M99
zbMATH DE Number: 5124473
zbMATH Keywords: effective descent morphism
zbMATH Keywords: factorization system
zbMATH Keywords: amalgamation property
zbMATH Keywords: topological categories
reviewed by: L. Márki
MaRDI profile type: Publication
full work available at URL: j.jpaa.2006.06.007
OpenAlex ID: W2058105841
cites work: Q4693062
cites work: Q5634589
cites work: Q3691902
cites work: Injective envelopes of Banach spaces
cites work: Categories of continuous functors. I
cites work: Six theorems about injective metric spaces
cites work: THE FUNDAMENTAL THEOREM OF GALOIS THEORY
cites work: Q3978975
cites work: Facets of descent. I
cites work: Monomorphisms, Epimorphisms, and Pull-Backs
cites work: Q3342632
cites work: Descent in categories of (co)algebras
cites work: The intersection property of amalgamations
cites work: Effective descent maps of topological spaces
cites work: Effective descent morphisms in some quasivarieties of algebraic, relational, and more general structures
cites work: Q4353284
cites work: Another approach to topological descent theory
cites work: Q3137167
cites work: Amalgamations in categories
cites work: Q4441921
cites work: Q3156487
cites work: Some categorical algebraic properties: counter-examples for functor categories
DOI: 10.1016/J.JPAA.2006.06.007
description: scientific article; zbMATH DE number 5124473