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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1984-0727257-2
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.


References [Enhancements On Off] (What's this?)

  • [CHR] M. Castellet, P. Hilton and J. Roitberg, On pseudo-identities. II (in preparation).
  • [HMR] Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. North-Holland Mathematics Studies, No. 15; Notas de Matemática, No. 55. [Notes on Mathematics, No. 55]. MR 0478146
  • [HR] Peter Hilton and Joseph Roitberg, On pseudo-identities. I, Arch. Math. (Basel) 41 (1983), no. 3, 204–214. MR 721051, https://doi.org/10.1007/BF01194830
  • [H] H. Hopf, Beiträge zur Klassifizierung der Flächenabbildungen, J. Reine Angew. Math. 165 (1931), 225-236.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0727257-2
Keywords: Epimorphism, monomorphism, Hopfian object, co-Hopfian object
Article copyright: © Copyright 1984 American Mathematical Society