Axiomatic Stable Homotopy Theory.

Intro -- Contents -- 1. Introduction and definitions -- 1.1. The axioms -- 1.2. Examples -- 1.3. Multigrading -- 1.4. Some basic definitions and results -- 2. Smallness, limits and constructibility -- 2.1. Notions of finiteness -- 2.2. Weak colimits and limits -- 2.3. Cellular towers and constructibility -- 3. Bousfield localization -- 3.1. Localization and colocalization functors -- 3.2. Existence of localization functors -- 3.3. Smashing and finite localizations -- 3.4. Geometric morphisms -- 3.5. Properties of localized subcategories -- 3.6. The Bousfield lattice -- 3.7. Rings, fields and minimal Bousfield classes -- 3.8. Bousfield classes of smashing localizations -- 4. Brown representability -- 4.1. Brown categories -- 4.2. Minimal weak colimits -- 4.3. Smashing localizations of Brown categories -- 4.4. A topology on [X, Y] -- 5. Nilpotence and thick subcategories -- 5.1. A naive nilpotence theorem -- 5.2. A thick subcategory theorem -- 6. Noetherian stable homotopy categories -- 6.1. Monochromatic subcategories -- 6.2. Thick subcategories -- 6.3. Localizing subcategories -- 7. Connective stable homotopy theory -- 8. Semisimple stable homotopy theory -- 9. Examples of stable homotopy categories -- 9.1. A general method -- 9.2. Chain complexes -- 9.3. he derived category of a ring -- 9.4. Homotopy categories of equivariant spectra -- 9.5. Cochain complexes of B-comodules -- 9.6. The stable category of B-modules -- 10. Future directions -- 10.1. Grading systems on stable homotopy categories -- 10.2. Other examples -- Appendix A. Background from category theory -- A.1. Triangulated categories -- A.2. Closed symmetric monoidal categories -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.