Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Epimorphisms and monomorphisms in homotopy


Author: Jerzy Dydak
Journal: Proc. Amer. Math. Soc. 116 (1992), 1171-1173
MSC: Primary 55N25; Secondary 55P10
MathSciNet review: 1124146
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55N25, 55P10

Retrieve articles in all journals with MSC: 55N25, 55P10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1124146-3
PII: S 0002-9939(1992)1124146-3
Keywords: Homotopy-epimorphisms, homotopy-monomorphisms, homotopy equivalences
Article copyright: © Copyright 1992 American Mathematical Society