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 (Vopěnkaʼs principle) is assumed true. It follows that, under the same assumptions, orthogonality sets...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2014-02, Vol.252, p.158-184
Main Authors: Casacuberta, Carles, Gutiérrez, Javier J., Rosický, Jiří
Format: Article
Language:English
Subjects:
Localizing subcategory
Stable homotopy category
Triangulated category
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Summary: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 (Vopěnkaʼs 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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2013.10.013