A note on the categorical van Kampen theorem
type: Item
instance of: scholarly article
title: A note on the categorical van Kampen theorem
zbMATH Open document ID: 1216.54003
author: Maria Manuel Clementino
published in: Topology and its Applications
publication date: 2011-05-16T00:00:00Z
review text: Brown and Janelidze identified the key property for obtaining the classical van Kampen theorem as a result on descent theory. In this note the author shows that for the canonical map \(X_1+X_2 \rightarrow X\), from the topological sum of two subspaces \(X_1,X_2\) of \(X\) into \(X\), to be of effective descent it is sufficient to be hereditarily a quotient map. Making use of the Brown-Janelidze categorical van Kampen theorem, this leads to a van Kampen-type result.
Mathematics Subject Classification ID: 54B15
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 5888196
zbMATH Keywords: effective descent morphism
zbMATH Keywords: triquotient map
zbMATH Keywords: van Kampen theorem
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
full work available at URL: j.topol.2011.01.011
OpenAlex ID: W2029433952
cites work: Q5200638
cites work: Van Kampen theorems for categories of covering morphisms in lextensive categories
cites work: Introduction to extensive and distributive categories
cites work: On finite triquotient maps
cites work: Triquotient maps via ultrafilter convergence
cites work: Effective descent morphisms in categories of lax algebras
cites work: A note on effective descent morphisms of topological spaces and relational algebras
cites work: Q5585132
cites work: Q3994935
cites work: Finite preorders and topological descent. I
cites work: Q3978975
cites work: Bi-quotient maps and Cartesian products of quotient maps
cites work: Complete spaces and tri-quotient maps
cites work: Localic triquotient maps are effective descent maps
cites work: Effective descent maps of topological spaces
DOI: 10.1016/J.TOPOL.2011.01.011
description: scientific article; zbMATH DE number 5888196