论文标题
模块类别子类别的有限和纯度
Finiteness and purity of subcategories of the module categories
论文作者
论文摘要
在本文中，通过使用函子和函子类别，我们研究了模块类别的子类别的有限和纯度。我们对有限表示类型的模块类别的违反有限分析子类别进行了表征。我们还表征了模块类别的违反有限解析子类别$λ$ {\ rm -mod}，该分类包含其函数类别的$λ$的$λ$的jacobson根部。我们研究了本地有限呈有限介绍的类别$ {\ budtrightArrow {\ lim}} \ Mathscr {x} $当$ \ Mathscr {x} $是协变量是$λ$ -MOD的有限量子类别时，$ -MATS $ $ $（x）有限地提出并给出了有限表示类型的协变量子类别的表征，其在过滤的colimits下的闭合特性方面。结果，我们研究了$ n $ - 集群倾斜子类别的有限和纯度以及模块类别的Gorenstein投影模块的子类别。这些结果扩展并统一了一些已知结果。
In this paper, by using functor rings and functor categories, we study finiteness and purity of subcategories of the module categories. We give a characterisation of contravariantly finite resolving subcategories of the module category of finite representation type in terms of their functor rings. We also characterize contravariantly finite resolving subcategories of the module category $Λ${\rm -mod} that contain the Jacobson radical of $Λ$ of finite type, by their functor categories. We study the pure semisimplicity conjecture for a locally finitely presented category ${\underrightarrow{\lim}}\mathscr{X}$ when $\mathscr{X}$ is a covariantly finite subcategory of $Λ$-mod and every simple object in Mod$(\mathscr{X}^{\rm op})$ is finitely presented and give a characterization of covariantly finite subcategories of finite representation type in terms of decomposition properties of their closure under filtered colimits. As a consequence we study finiteness and purity of $n$-cluster tilting subcategories and the subcategory of the Gorenstein projective modules of the module categories. These results extend and unify some known results.
