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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on epimorphisms and monomorphisms in homotopy theory


Authors: Peter Hilton and Joseph Roitberg
Journal: Proc. Amer. Math. Soc. 90 (1984), 316-320
MSC: Primary 55P10; Secondary 55P30
MathSciNet review: 727257
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Abstract: We study epimorphisms $ e:X \to X$ and monomorphisms $ m:X \to X$ in the pointed homotopy category of path-connected CW-spaces. Our principal theorems allow us to infer that under suitable finiteness and fundamental group assumptions, such are in fact homotopy equivalences.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0727257-2
PII: S 0002-9939(1984)0727257-2
Keywords: Epimorphism, monomorphism, Hopfian object, co-Hopfian object
Article copyright: © Copyright 1984 American Mathematical Society