Editing CW complex (section)

=='The' homotopy category==

The [[homotopy category]] of CW complexes is, in the opinion of some experts, the best if not the only candidate for ''the'' homotopy category (for technical reasons the version for [[pointed space]]s is actually used).<ref>For example, the opinion "The class of CW complexes (or the class of spaces of the same homotopy type as a CW complex) is the most suitable class of topological spaces in relation to homotopy theory" appears in {{SpringerEOM| title=CW-complex | id=CW-complex | oldid=15603 | first=D.O. | last=Baladze }}</ref> Auxiliary constructions that yield spaces that are not CW complexes must be used on occasion. One basic result is that the [[representable functor]]s on the homotopy category have a simple characterisation (the [[Brown representability theorem]]).

See also: [[Milnor's theorem on Kan complexes]]