Silting theory in triangulated categories with coproducts
نویسندگان
چکیده
منابع مشابه
Silting mutation in triangulated categories
In representation theory of algebras the notion of ‘mutation’ often plays important roles, and two cases are well known, i.e. ‘cluster tilting mutation’ and ‘exceptional mutation’. In this paper we focus on ‘tilting mutation’, which has a disadvantage that it is often impossible, i.e. some of summands of a tilting object can not be replaced to get a new tilting object. The aim of this paper is ...
متن کاملOn Silting-discrete Triangulated Categories
The aim of this paper is to study silting-discrete triangulated categories. We establish a simple criterion for silting-discreteness in terms of 2-term silting objects. This gives a powerful tool to prove silting-discreteness of finite dimensional algebras. Moreover, we will show Bongartz-type Lemma for silting-discrete triangulated categories.
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...
متن کاملAuslander-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...
متن کاملThe K-Theory of Triangulated Categories
4.1 Historical Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014 4.3 Waldhausen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2019
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2018.07.016