## Note on epimorphisms and monomorphisms in homotopy theory.(English)Zbl 0565.55009

The paper deals with Hopfian and co-Hopfian objects in the pointed homotopy category $${\mathcal K}$$ of path-connected CW-spaces. An object X of a category $${\mathcal C}$$ is called Hopfian if every epimorphism $$\epsilon$$ : $$X\twoheadrightarrow X$$ in $${\mathcal C}$$ is an automorphism. In the principal theorem it is proved that Hopfian and co-Hopfian objects in $${\mathcal K}$$ can be obtained under suitable finiteness conditions on homology and fundamental group assumptions.
Reviewer: K.H.Kamps

### MSC:

 55P10 Homotopy equivalences in algebraic topology 55P30 Eckmann-Hilton duality 20F18 Nilpotent groups 55P99 Homotopy theory 55P20 Eilenberg-Mac Lane spaces
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### References:

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