From triangulated categories to module categories via localization II: calculus of fractions
نویسندگان
چکیده
منابع مشابه
From triangulated categories to module categories via localization II: calculus of fractions
We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(T,−), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admits a calculus of left and right fractions. It follows that the Gabriel–Zisman localization of the quotient at the class of regular morphisms is abelian. We show that it is equiv...
متن کاملFrom triangulated categories to module categories via localisation II: calculus of fractions
We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(T, −), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equiv...
متن کاملLocalization for Triangulated Categories
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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The results in this note are all from [Nee01] or [BN93]. For necessary background on cardinals (particularly regular and singular cardinals) see our notes on Basic Set Theory (BST). In our BST notes there is no mention of grothendieck universes, whereas all our notes on category theory (including this one) are implicitly working inside a fixed grothendieck universe U using the conglomerate conv...
متن کاملLocalization Theory for Triangulated Categories
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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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2012
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms/jdr077