Monomorphisms and epimorphisms in homotopy theory (Q1058754)
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scientific article; zbMATH DE number 3901629
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Monomorphisms and epimorphisms in homotopy theory |
scientific article; zbMATH DE number 3901629 |
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Monomorphisms and epimorphisms in homotopy theory (English)
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1983
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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.
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homotopy equivalence
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path-connected CW-spaces
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Hopfian group
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Hopfian object
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epimorphisms
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monomorphisms
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co-Hopfian objects
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nilpotent spaces of finite type
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