论文标题
从扭转类的晶格到广泛的子类别和冰封型子类别的posets
From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
论文作者
论文摘要
在本文中，我们通过在完全半分布的lattice中使用kappa映射，以纯粹的晶格理论方式计算以纯晶格理论方式的扭转类别晶格的广泛子类别和冰封的子类别。至于广泛的子类别的poset，我们通过具有规范联接表示的宽子类别和扭转类之间的培养，从而提供了两个更简单的结构。更准确地说，对于完全半分布的晶格，我们提供了两个带有规范联接表示形式的元素的Poset结构：Kappa订单（使用Barnard-todorov-todorov-Zhu的扩展Kappa映射定义）和核心标签订单（将Shard shard交叉点列出了出色的订单订单订单，以获得出色的latters-Sirolubil-Sirorrun-Sirolufice-Lattices）。然后，我们证明了扭转类别晶格的这些poset是一致的，并且与宽子类别的poset是同构的。作为副产品，我们使用扩展的Kappa地图对有限的Coxeter组上的碎片相交顺序进行了简单描述。
In this paper, we compute the posets of wide subcategories and ICE-closed subcategories from the lattice of torsion classes in an abelian length category in a purely lattice-theoretical way, by using the kappa map in a completely semidistributive lattice. As for the poset of wide subcategories, we give two more simple constructions via a bijection between wide subcategories and torsion classes with canonical join representations. More precisely, for a completely semidistributive lattice, we give two poset structures on the set of elements with canonical join representations: the kappa order (defined using the extended kappa map of Barnard--Todorov--Zhu), and the core label order (generalizing the shard intersection order for congruence-uniform lattices). Then we show that these posets for the lattice of torsion classes coincide and are isomorphic to the poset of wide subcategories. As a byproduct, we give a simple description of the shard intersection order on a finite Coxeter group using the extended kappa map.
