Auslander–Buchweitz Approximation Theory for Triangulated Categories
نویسندگان
چکیده
منابع مشابه
Auslander-Buchweitz Approximation Theory for Triangulated Categories
We introduce and develop an analogous of the AuslanderBuchweitz approximation theory (see [2]) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category T , which are based on the behavior of certain subcategories under finiteness of resolutions and vanishin...
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Contents 1. Introduction 1 2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 14 5. Localization via Brown representability 24 6. Well generated triangulated categories 31 7. Localization for well generated categories 39 8. Epilogue: Beyond well generatedness 47 Appendix A. The abelianization of a triangulated category 4...
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4.1 Historical Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014 4.3 Waldhausen...
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Contents 1. Introduction 1 2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 13 5. Localization via Brown representatbility 23 6. Well generated triangulated categories 31 7. Localization for well generated categories 38 8. Epilogue: Beyond well-generatedness 46 Appendix A. The abelianization of a triangulated category ...
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This is an edited extract from my paper [11]. We define triangulated categories and discuss homotopy pushouts and pullbacks in such categories in §1 and §2. We focus on Verdier’s octahedral axiom, since the axiom that is usually regarded as the most substantive one is redundant: it is implied by Verdier’s axiom and the remaining, less substantial, axioms. Strangely, since triangulated categorie...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2011
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-011-9261-4