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Homotopy epimorphisms and Lusternik-Schnirelmann category


Author: James A. Draper
Journal: Proc. Amer. Math. Soc. 50 (1975), 471-476
MSC: Primary 55C30
DOI: https://doi.org/10.1090/S0002-9939-1975-0367983-5
MathSciNet review: 0367983
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Abstract: This paper examines the relationship of the Lusternik-Schnirelmann category and related numerical homotopy invariants to the epimorphisms in the homotopy category. The results are of the form: if $ N$ is a numerical homotopy invariant and $ f:X \to Y$ is an epimorphism, then under certain hypotheses $ N(X) \geq N(Y)$. The Eckmann-Hilton dual of the main result is also included; as a corollary, a criterion is given for a categorical subobject of an $ H$-space to be an $ H$-space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0367983-5
Keywords: Homotopy epimorphism, homotopy monomorphism, Lusternik-Schnirelmann category, cocategory, conilpotency, weak category, cuplength
Article copyright: © Copyright 1975 American Mathematical Society

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