Are all localizing subcategories of stable homotopy categories coreflective?

Carles Casacuberta; Javier J. Gutiérrez; Jiří Rosický

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arXiv · 1106.2218

Are all localizing subcategories of stable homotopy categories coreflective?

Carles Casacuberta·Javier J. Gutiérrez·Jiří Rosický

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Abstract

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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BibTeX RIS

Carles Casacuberta, Javier J. Gutiérrez, Jiří Rosický. 2012-04-13. Are all localizing subcategories of stable homotopy categories coreflective?. https://arxiv.org/abs/1106.2218

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