Journal of Mathematics and Statistics

A Note on “The Homotopy Category is a Homotopy Category”

Afework Solomon

DOI : 10.3844/jmssp.2019.201.207

Journal of Mathematics and Statistics

Volume 15, 2019

Pages 201-207


In his paper with the title, “The Homotopy Category is a Homotopy Category”, Arne Strøm shows that the category Top of topo- logical spaces satisfies the axioms of an abstract homotopy category in the sense of Quillen. In this study, we show by examples that Quillen’s model structure on Top fails to capture some of the subtleties of classical homotopy theory and also, we show that the whole of classical homo-topy theory cannot be retrieved from the axiomatic approach of Quillen. Thus, we show that model category is an incomplete model of classical homotopy theory.


© 2019 Afework Solomon. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.