J. Rosický1
Localizing subcategories are very important in stable homotopy theory and
there is not known any example of a localizing subcategory
without a localization functor, which is the same thing as
not
being coreflective. We will confirm the suspicion of M. Hovey, J. H.
Palmieri and N. P. Strickland that the answer may depend on set theory
by showing that, assuming Vopěnka's principle, every localizing
subcategory
of the homotopy category
of spectra is
coreflective. Moreover,
is generated by a single object and,
dually, every colocalizing subcategory
of
is reflective
and generated by a single object. The consequence is that every localizing
subcategory of
is a cohomological Bousfield class.