# Are all localizing subcategories of a stable homotopy category coreflexive?

Masaryk University, Brno

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.

#### Footnotes

- ...ý
^{1}
- joint work with C. Casacuberta and J. Gutiérrez

2005-05-23