Monomorphisms and epimorphisms in homotopy theory
type: Item
instance of: scholarly article
title: Monomorphisms and epimorphisms in homotopy theory
zbMATH Open document ID: 0565.55010
DOI: 10.1007/BF02761953
author: Joseph Roitberg
published in: Israel Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The author improves the results in his paper with \textit{P. Hilton} [see the preceding review] on Hopfian and co-Hopfian objects in the pointed homotopy category \({\mathcal K}\) of path-connected CW-spaces by replacing finiteness conditions on homology by Hopficity conditions. Furthermore the question is studied of when a morphism \(f: X\to Y\) in \({\mathcal K}\) which is simultaneously mono and epi is actually iso and general conditions are given. This holds for instance if X and Y are nilpotent spaces of finite type.
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 55P30
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 55P20
Mathematics Subject Classification ID: 55P99
zbMATH DE Number: 3901629
zbMATH Keywords: homotopy equivalence
zbMATH Keywords: path-connected CW-spaces
zbMATH Keywords: Hopfian group
zbMATH Keywords: Hopfian object
zbMATH Keywords: epimorphisms
zbMATH Keywords: monomorphisms
zbMATH Keywords: co-Hopfian objects
zbMATH Keywords: nilpotent spaces of finite type
MaRDI profile type: Publication
cites work: Shorter Notes: The Whitehead Theorem for Nilpotent Spaces
cites work: Note on Epimorphisms and Monomorphisms in Homotopy Theory
cites work: Q4086427
cites work: Residual finiteness in homotopy theory
cites work: Genetics of homotopy theory and the Adams conjecture
description: scientific article; zbMATH DE number 3901629