论文标题
冰封子类别和广泛的$τ$ - 使用模块
ICE-closed subcategories and wide $τ$-tilting modules
论文作者
论文摘要
在本文中，我们研究了使用扭转类别的Abelian长度类别的冰封（=图像 - 塞尔内尔 - 扩张）子类别。在扭转类的晶格中，每个间隔$ [\ MATHCAL {u}，\ MATHCAL {T}] $，我们将一个子类别$ \ Mathcal {T} \ Cap \ Cap \ Mathcal {U}^\ Perp $称为心脏。我们表明，每个冰断的子类别都可以成为扭转类别间隔的核心，并给出一个晶格理论的特征，其心脏被冰断的间隔。特别是，我们证明了冰断的子类别是一些广泛的子类别中的扭转类。对于Artin代数，我们介绍了宽$τ$的模块的概念，作为支撑$τ$的概括 - 替代模块。然后，我们建立了宽$τ$ tisting模块和双重有限冰封闭的子类别之间的两者，该子类别扩展了adachi-iyama-iyama-reiten对扭转类别的培养。对于遗传病例，我们通过引入刚性模块的突变来讨论冰断子类别的poset的震颤。
In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of an abelian length category using torsion classes. To each interval $[\mathcal{U},\mathcal{T}]$ in the lattice of torsion classes, we associate a subcategory $\mathcal{T} \cap \mathcal{U}^\perp$ called the heart. We show that every ICE-closed subcategory can be realized as a heart of some interval of torsion classes, and give a lattice-theoretic characterization of intervals whose hearts are ICE-closed. In particular, we prove that ICE-closed subcategories are precisely torsion classes in some wide subcategories. For an artin algebra, we introduce the notion of wide $τ$-tilting modules as a generalization of support $τ$-tilting modules. Then we establish a bijection between wide $τ$-tilting modules and doubly functorially finite ICE-closed subcategories, which extends Adachi--Iyama--Reiten's bijection on torsion classes. For the hereditary case, we discuss the Hasse quiver of the poset of ICE-closed subcategories by introducing a mutation of rigid modules.
