Abelian categories arising from cluster tilting subcategories II: quotient functors
نویسندگان
چکیده
منابع مشابه
2 3 M ay 2 00 7 From triangulated categories to abelian categories – cluster tilting in a general framework
A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.
متن کامل0 Fe b 20 07 From triangulated categories to abelian categories – cluster tilting in a general framework Steffen
A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.
متن کاملABELIAN CATEGORIES ARISING FROM A MAXIMAL n-ORTHOGONAL SUBCATEGORY
As Koenig and Zhu showed, quotient of a triangulated category by a maximal 1-orthogonal subcategory becomes an abelian category. In this paper, we generalize this result to a maximal n-orthogonal subcategory for an arbitrary positive integer n.
متن کاملAlmost Complete Cluster Tilting Objects in Generalized Higher Cluster Categories
We study higher cluster tilting objects in generalized higher cluster categories arising from dg algebras of higher Calabi-Yau dimension. Taking advantage of silting mutations of Aihara-Iyama, we obtain a class of m-cluster tilting objects in generalized m-cluster categories. For generalized m-cluster categories arising from strongly (m + 2)-Calabi-Yau dg algebras, by using truncations of minim...
متن کاملCluster tilting objects in generalized higher cluster categories
We prove the existence of an m-cluster tilting object in a generalized m-cluster category which is (m+1)-Calabi–Yau andHom-finite, arising froman (m+2)-Calabi–Yau dg algebra. This is a generalization of the result for them = 1 case in Amiot’s Ph.D. thesis. Our results apply in particular to higher cluster categories associated to Ginzburg dg categories coming from suitable graded quivers with s...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
سال: 2019
ISSN: 0308-2105,1473-7124
DOI: 10.1017/prm.2019.42