Une remarque sur le classifiant d'une catégorie topologique. (A remark on the classifying space of a topological category)
type: Item
instance of: scholarly article
title: Une remarque sur le classifiant d'une catégorie topologique. (A remark on the classifying space of a topological category)
zbMATH Open document ID: 0603.55018
DOI: 10.1007/BF01194006
author: B. George
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: The author answers a question of R. Brown concerning pushouts (amalgamated sums) of topological categories. The main result is as follows. Let \({\mathcal F}\) be a topological category with objects X and \(f: X\to Y\) a map. Consider X and Y as topological categories. Then the pushout \({\mathcal G}\) of the diagram \({\mathcal F}\leftarrow X\to Y\) has a classifying space \({\mathcal B}{\mathcal G}\) which is weakly homotopy equivalent to the pushout of B\({\mathcal F}\leftarrow BX\to BY\), that is, B and \({\mathcal G}\) commute on such diagrams. The author works in the category of k-spaces and for the proof requires that certain natural inclusions in the nerve of F be cofibrations or h- cofibrations. This condition T is observed to be natural in several concrete cases. The main technical ingredient of the proof is a specific construction of the pushout category \({\mathcal G}\).
Mathematics Subject Classification ID: 55U40
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55P05
Mathematics Subject Classification ID: 18F99
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 3973849
zbMATH Keywords: pushouts of topological categories
zbMATH Keywords: classifying space
reviewed by: Solomon Jekel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3973849