Triangulated quotient categories revisited
WebA notion of mutation of subcategories in an extriangulated category is defined in this article. Let $\cal A$ be an extension closed subcategory of an extriangulated category $\cal C$. Then the quotient category $\cal M:=\cal{A}/\cal{X}$ carries naturally a triangulated structure whenever $(\cal A,\cal A)$ forms an $\cal X$-mutation pair. http://home.ustc.edu.cn/~xwchen/Personal%20Papers/quotient%20triangulated%20categories.pdf
Triangulated quotient categories revisited
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WebAug 10, 2024 · We investigate abelian quotients arising from extriangulated categories via morphism categories, which is a unified treatment for both exact categories and … WebAug 1, 2016 · Triangulated quotient categories revisited. Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories …
WebA notion of mutation of subcategories in a right triangulated category is defined in this paper. When (Z,Z) is a D−mutation pair in a right triangulated category C, the quotient category Z/D carries naturally a right triangulated structure. Moreover, if the right triangulated category satisfies some reasonable conditions, then the right triangulated … WebNakaoka and Y. Palu, Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories (2016), arXiv:1605.05607. Google Scholar; 10. L. Salce, Cotorsion theories for abelian groups, Symposia Math. 23 (1979) 11–32. Google Scholar; 11. P. Zhou and B. Zhu, Triangulated quotient categories revisited, J. Algebra 502 (2024 ...
WebExtriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of mutation … WebA notion of mutation of subcategories in a right triangulated category is defined in this paper. When (Z,Z) is a D−mutation pair in a right triangulated category C, the quotient …
WebJan 9, 2024 · Yang X Y, Wang Z C. Proper resolutions and Gorensteiness in triangulated categories. Rocky Mountain J Math, 2024, 47: 1013–1053. Article MathSciNet Google Scholar Zhou P Y, Zhu B. Triangulated quotient categories revisited. J Algebra, 2024, 502: 196–232. Article MathSciNet Google Scholar
WebAug 1, 2016 · Triangulated quotient categories revisited @article{Zhou2016TriangulatedQC, title={Triangulated quotient categories revisited}, author={Panyue Zhou and Bin Zhu}, … dj buzz fuzzWebAug 1, 2024 · The notions of n -abelian and n -exact categories were introduced by Jasso in [8]. An important source of examples of n -abelian and n -exact categories are n -cluster tilting subcategories. For they specialise to abelian and exact categories. Jacobsen and Jørgensen [10] proved that any quotient of an -angulated category with a Serre functor ... dj bxbWebJul 31, 2016 · Some of these constructions had been worked, for instance, in [12,5] where it is established that, under certain conditions, quotients categories carry triangulated … beclometason mesalazine klysma bijwerkingenWebMay 6, 2024 · Properties of triangulated and quotient categories arising from. -Calabi-Yau triples. The original definition of cluster algebras by Fomin and Zelevinsky has been categorified and generalised in several ways over the course of the past 20 years, giving rise to cluster theory. This study lead to Iyama and Yang's generalised cluster categories ... becmi bardWebas triangulated categories to the relevant u-cluster categories. As a backdrop to this, I will show more generally, under some technical assump-tions, that if T is a triangulated category with a class of objects X, then the quotient category TX is triangulated if and only if X is equal to its image under the Auslander–Reiten translation of T ... beclimb malaga reservaWeb—Let T be a triangulated category. Show that any triangle of the form: X Y Z 0 TX is isomorphic to a triangle of the form: X X Z Z 0 TX 2.Triangulated functors and Verdier quotient Here, we introduce morphisms of triangulated categories, triangulated subcate-gories, and quotients. Definition 2.1. —Let (T,T) and (T0,T0) be dj buzztimeWebTriangulated quotient categories revisited∗ Panyue Zhou and Bin Zhu Abstract Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of mutation of subcategories in an extriangulated category is defined in this article. dj bx\\u0027treme