Abelian quotients of triangulated categories
Abelian quotients of triangulated categories
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DOI：
10.1016/j.jalgebra.2015.04.042
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发表时间：
2015-01
影响因子：
0.9
通讯作者：
B. Grimeland;Karin M. Jacobsen
中科院分区：
文献类型：
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作者：
B. Grimeland;Karin M. Jacobsen
我们研究了交换商范畴A=T/J，其中T是三角范畴，J是T的理想。在商函子是上同调的假设下，我们证明了它是可表示的，并给出了函子的显式刻画。我们给出了可表示函子是商函子的技术准则，以及J何时产生T的一个簇倾斜子范畴的一个准则。我们证明了商函子保持AR-结构。作为应用，我们证明了如果T是有限的2-Calabi-Yau范畴，则除极少数例外J是T的一个簇倾斜子范畴。
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.