论文标题
$ \ mathrm {hom} $的平衡系统
Balanced systems for $\mathrm{Hom}$
论文作者
论文摘要
从相对同源代数中（CO）发电机的概念中，我们提出有限平衡系统$ [（\ Mathcal {x}，ω）的概念; （ν，\ Mathcal {y}）] $作为诱导平衡对$（\ Mathcal {X}}，\ Mathcal {y}）$的工具，用于$ \ Mathrm {homrm {homm {hom} $ fuctors with domain with domain，由相对于$ \ nathcal {x} $的同源尺寸确定的域确定。 这种平衡方法将涵盖几个众所周知的环境，其中$ \ mathrm {hom} $的正确衍生函数相对于阿贝尔类别中的某些对象，例如Gorenstein Projective和Injective模块和连锁复合物，Gorenstein模块，相对于Auslander和Bass类，等等。
From the notion of (co)generator in relative homological algebra, we present the concept of finite balanced system $[(\mathcal{X} , ω); (ν, \mathcal{Y})]$ as a tool to induce balanced pairs $(\mathcal{X} , \mathcal{Y} )$ for the $\mathrm{Hom}$ functor with domain determined by the finiteness of homological dimensions relative to $\mathcal{X}$ and $\mathcal{Y}$. This approach to balance will cover several well known ambients where right derived functors of $\mathrm{Hom}$ are obtained relative to certain classes of objects in an abelian category, such as Gorenstein projective and injective modules and chain complexes, Gorenstein modules relative to Auslander and Bass classes, among others.
