Monomorphisms and epimorphisms in homotopy theory
Copyright policy )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.
- City University of New York United States
- Hunter College United States
- King’s University United States
Eilenberg-Mac Lane spaces, monomorphisms, epimorphisms, Hopfian group, Homotopy theory, Nilpotent groups, homotopy equivalence, path-connected CW-spaces, co-Hopfian objects, Homotopy equivalences in algebraic topology, Eckmann-Hilton duality, nilpotent spaces of finite type, Hopfian object
Eilenberg-Mac Lane spaces, monomorphisms, epimorphisms, Hopfian group, Homotopy theory, Nilpotent groups, homotopy equivalence, path-connected CW-spaces, co-Hopfian objects, Homotopy equivalences in algebraic topology, Eckmann-Hilton duality, nilpotent spaces of finite type, Hopfian object
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