General Heart Construction on a Triangulated Category (II): Associated Homological Functor
General Heart Construction on a Triangulated Category (II): Associated Homological Functor
复制标题
DOI：
10.1007/s10485-010-9226-z
复制
发表时间：
2009-10
影响因子：
0.6
通讯作者：
N. Abe;H. Nakaoka
中科院分区：
文献类型：
--
作者：
N. Abe;H. Nakaoka
在本文的前一部分（I）中，我们证明了对于任何挠对（即，在一个三角范畴中，存在一个相关联的阿贝尔范畴，我们称之为心范畴。扭对的两种极端情形是-结构和集团倾斜子范畴。如果扭对来自于at结构，那么它的心脏就是这个结构的心脏。在这种情况下，正如所知，通过构造某些伴随函子，我们得到了从三角范畴到心的同调函子。如果挠对来自一个簇倾斜子范畴，则它的心与这个子范畴的三角化范畴的商范畴重合。在这种情况下，商函子成为同调的。在本文中，我们统一了这两种构造，得到了一个从三角范畴到任意挠对的心的同调函子。
In the preceding part (I) of this paper, we showed that for any torsion pair (i.e.,t-structure without the shift-closedness) in a triangulated category, there is an associated abelian category, which we call theheart. Two extremal cases of torsion pairs aret-structures and cluster tilting subcategories. If the torsion pair comes from at-structure, then its heart is nothing other than the heart of thist-structure. In this case, as is well known, by composing certain adjoint functors, we obtain a homological functor from the triangulated category to the heart. If the torsion pair comes from a cluster tilting subcategory, then its heart coincides with the quotient category of the triangulated category by this subcategory. In this case, the quotient functor becomes homological. In this paper, we unify these two constructions, to obtain a homological functor from the triangulated category, to the heart of any torsion pair.