Are all localizing subcategories of stable homotopy categories   coreflective?
  We prove that, in a triangulated category with combinatorial models, every localizing subcategory is coreflective and every colocalizing subcategory is reflective if a certain large-cardinal axiom (Vopenka's principle) is assumed true. It follows that, under the same assumptions, orthogonality sets up a bijective correspondence between localizing subcategories and colocalizing subcategories. The existence of such a bijection was left as an open problem by Hovey, Palmieri and Strickland in their axiomatic study of stable homotopy categories and also by Neeman in the context of well-generated triangulated categories. 
Carles Casacuberta, Javier J. Guti\'errez and Ji\v{r}\'i Rosick\'y
math.CT math.AG math.AT