论文标题
Monobrick，一种统一的无扭转课程和广泛的子类别的方法
Monobrick, a uniform approach to torsion-free classes and wide subcategories
论文作者
论文摘要
对于长度的Abelian类别，我们显示所有无扭转类都可以通过仅使用砖上的信息（包括非功能限制的砖块）进行分类。这个想法是考虑无扭转类中的简单对象集，该类别具有以下属性：它是一组砖块，其中每个非零地图都是注入。我们称这样的套件为千禧一代。在本文中，我们提供了一种统一的方法，可以通过Monobricks研究无扭转类和广泛的子类别。我们表明，MONOBRICKS与左Schur子类别进行了两次射击，其中包含在扩展，内核和图像下关闭的所有子类别，因此统一了无扭转的类别和广泛的子类别。然后，我们表明无扭转的类别对应于骨封闭的千禧一代。使用MONOBRICKS，我们在长度的Abelian类别中推断出关于扭转（ - Free）类（例如有限的结果和两种物品）的较广泛的子类别（例如，有限结果和两种物品）的几个已知结果，而无需使用$τ$ tishting理论。对于Nakayama代数，左Schur子类别与在扩展，内核和图像下关闭的子类别相同，我们表明其数字与较大的Schröder数字有关。
For a length abelian category, we show that all torsion-free classes can be classified by using only the information on bricks, including non functorially-finite ones. The idea is to consider the set of simple objects in a torsion-free class, which has the following property: it is a set of bricks where every non-zero map between them is an injection. We call such a set a monobrick. In this paper, we provide a uniform method to study torsion-free classes and wide subcategories via monobricks. We show that monobricks are in bijection with left Schur subcategories, which contains all subcategories closed under extensions, kernels and images, thus unifies torsion-free classes and wide subcategories. Then we show that torsion-free classes bijectively correspond to cofinally closed monobricks. Using monobricks, we deduce several known results on torsion(-free) classes and wide subcategories (e.g. finiteness result and bijections) in length abelian categories, without using $τ$-tilting theory. For Nakayama algebras, left Schur subcategories are the same as subcategories closed under extensions, kernels and images, and we show that its number is related to the large Schröder number.
