Are all localizing subcategories of stable homotopy categories coreflective?

Details Are all localizing subcategories of stable homotopy categories coreflective? Are all localizing subcategories of stable homotopy categories coreflective?

2011-06-11

arxiv.org/abs/1106.2218v3

Mathematics

Category Theory

29 pages; a few changes made in Section 2

Scientific paper

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.

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