Epimorphisms and monomorphisms in homotopy
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- by Jerzy Dydak PDF
- Proc. Amer. Math. Soc. 116 (1992), 1171-1173 Request permission
Abstract:
The main result of this note is the following: Theorem A. If $f:X \to Y$ is an epimorphism of $\mathcal {H}\mathcal {C}{\mathcal {W}^*}$, the homotopy category of pointed path-connected CW-spaces, and ${\pi _1}(f):{\pi _1}(X) \to {\pi _1}(Y)$ is a monomorphism, then $\tilde f:\tilde X \to \tilde Y$ is an epimorphism of $\mathcal {H}\mathcal {C}{\mathcal {W}^*}$. As a straightforward consequence the following results of Dyer-Roitberg (Topology Appl. (to appear)) is derived: Theorem B. A map $f:X \to Y$ is an equivalence in $\mathcal {H}\mathcal {C}{\mathcal {W}^*}$, the homotopy category of pointed path-connected CW-spaces, iff it is both an epimorphism and a monomorphism in $\mathcal {H}\mathcal {C}{\mathcal {W}^*}$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 1171-1173
- MSC: Primary 55N25; Secondary 55P10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1124146-3
- MathSciNet review: 1124146