Monomorphisms and epimorphisms in homotopy theory
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.
scientific article; zbMATH DE number 3901629