03558nam 2200577 450 991081188870332120170822144143.01-4704-0195-9(CKB)3360000000464794(EBL)3114506(SSID)ssj0000888784(PQKBManifestationID)11462801(PQKBTitleCode)TC0000888784(PQKBWorkID)10881851(PQKB)10253717(MiAaPQ)EBC3114506(RPAM)4488445(PPN)195414934(EXLCZ)99336000000046479419970312h19971997 uy| 0engur|n|---|||||txtccrAxiomatic stable homotopy theory /Mark Hovey, John H. Palmieri, Neil P. StricklandProvidence, Rhode Island :American Mathematical Society,[1997]©19971 online resource (130 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 610"July 1997, volume 128, number 610 (second of 4 numbers)."0-8218-0624-6 Includes bibliographical references (pages 109-111) and index.""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 Bâ€?comodules""; ""9.6. The stable category of Bâ€?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""Memoirs of the American Mathematical Society ;no. 610.Homotopy theoryHomotopy theory.510 s514/.24Hovey Mark1965-62160Palmieri John H(John Harold),1964-Strickland Neil P.1966-MiAaPQMiAaPQMiAaPQBOOK9910811888703321Axiomatic stable homotopy theory4025731UNINA