Talk:Homotopy category

Homotopy categories of model categories.
It seems to me that this description of a homotopy category is too narrow. From the current perspective homotopy categories are usually understood in the context of model categories. For a model category M its homotopy category is equivalent to the category constructed by taking the full subcategory of M on fibrant-cofibrant objects and then inverting all weak equivalences. As a result one does not need to argue which homotopy category is "the" homotopy category - there is one for each model category. One ("Serre") model category structure on the category of topological spaces yields the homotopy category equivalent to the category of CW-complexes and homotopy classes of maps between CW-complexes. Another ("Hurewicz") model category structure on topological spaces produces the homotopy category equivalent to the category of all spaces with homotopy classes of maps as morphisms. --69.204.54.113 (talk) 05:27, 22 August 2008 (UTC)

Assessment comment
Substituted at 02:13, 5 May 2016 (UTC)