On the functors \(CW_ A\) and \(P_ A\)
type: Item
instance of: scholarly article
title: On the functors \(CW_ A\) and \(P_ A\)
zbMATH Open document ID: 0873.55014
DOI: 10.1215/S0012-7094-96-08419-7
author: Wojciech Chachólski
published in: Duke Mathematical Journal
publication date: 1997-10-30T00:00:00Z
review text: Given a pointed space \(A\) and a map \(f:X\to Y\) consider its factorization \(X\to Y'@>p>>Y\), where \((Y',X)\) is a relative \(A\)-CW-complex and \(p\) a map inducing a weak equivalence \(p_*:\text{TOP}(A,Y')\to \text{TOP}(A,Y)\) of mapping spaces. In particular, for the maps \(*\to X\) and \(X\to*\) we get maps \(CW_AX\to X\) and \(X\to P_AX\), respectively. The author applies the results by \textit{E. Dror Farjoun} [Cellular inequalities, Contemp. Math. 181, 159-181 (1995)] to study the relationship between the functors \(CW_A\) and \(P_A\). It is shown that the kernel of \(P_A\) is the closure, under taking extensions by fibrations, of the image of \(CW_A\) and various weak cellular inequalities are presented.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 55U10
Mathematics Subject Classification ID: 18G30
Mathematics Subject Classification ID: 55P99
zbMATH DE Number: 943720
zbMATH Keywords: acyclic (null)-simplicial set
zbMATH Keywords: cellular inequality
zbMATH Keywords: relative CW-complex
MaRDI profile type: Publication
cites work: Localization and Periodicity in Unstable Homotopy Theory
cites work: Homotopy limits, completions and localizations
cites work: Q4870921
cites work: Q4327001
cites work: Cellular spaces, null spaces and homotopy localization
cites work: Q4156432
cites work: Q5639839
cites work: Q5550390
cites work: Homotopical algebra
full work available at URL: s0012-7094-96-08419-7
OpenAlex ID: W1505253472
description: scientific article; zbMATH DE number 943720