Abelian quotients of triangulated categories
| Autor: | Benedikte Grimeland, Karin Marie Jacobsen |
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| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Pure mathematics Fiber functor Algebra and Number Theory Functor Brown's representability theorem Representable functor Functor category Cone (category theory) Mathematics::Algebraic Topology Mathematics::K-Theory and Homology Mathematics::Category Theory Natural transformation FOS: Mathematics Representation Theory (math.RT) Exact functor Mathematics - Representation Theory Mathematics |
| Zdroj: | Journal of Algebra. 439:110-133 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2015.04.042 |
| Popis: | We study abelian quotient categories A=T/J, where T is a triangulated category and J is an ideal of T. Under the assumption that the quotient functor is cohomological we show that it is representable and give an explicit description of the functor. We give technical criteria for when a representable functor is a quotient functor, and a criterion for when J gives rise to a cluster-tilting subcategory of T. We show that the quotient functor preserves the AR-structure. As an application we show that if T is a finite 2-Calabi-Yau category, then with very few exceptions J is a cluster-tilting subcategory of T. 20 pages. Minor changes; have stated more explicitly where finiteness is required |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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