论文标题
扩展（$τ$ - ）倾斜子类别和（CO）淤泥模块
Extending ($τ$-)tilting subcategories and (co)silting modules
论文作者
论文摘要
让$ b $为有限维数代数，$ a = b [p_0] $是$ b $的单点扩展代数，相对于有限生成的投影$ b $ -b $ -module $ p_0 $。 $ b $ modules和$ a $ modules的类别与两个伴随函数$ \ MATHCAL {r} $和$ \ MATHCAL {E} $相关，分别称为限制和扩展名函数。基于这两个函子的良好同源属性，已经研究了一些概念的限制和扩展，例如倾斜和$τ$ - 施用模块，以有限呈现的模块（即小型mod）类别进行了研究。在本文中，我们研究了倾斜和支持$τ$的行为，相对于这两个函数。此外，我们研究了特殊相关模块的限制和扩展，例如Finendo准倾斜模块，Silting模块和固定模块。我们的研究将在所有模块的类别中进行，这将称为大型模块。基于此类研究，除了新的结果外，经典结果还扩大了，不仅从模块到子类别，而且还从小型mod到大型mod。
Let $B$ be a finite dimensional algebra and $A=B[P_0]$ be the one-point extension algebra of $B$ with respect to the finitely generated projective $B$-module $P_0$. The categories of $B$-modules and $A$-modules are related by two adjoint functors $\mathcal{R}$ and $\mathcal{E}$, called the restriction and the extension functors, respectively. Based on the nice homological properties of these two functors, restriction and extension of some notions such as tilting and $τ$-tilting modules have been studied in the category of finitely presented modules, i.e. small mod. In this paper, we investigate the behaviour of tilting and support $τ$-tilting subcategories with respect to these two functors. Moreover, we investigate the restriction and the extension of special related modules such as finendo quasi-tilting modules, silting modules, and cosilting modules. Our studies will be done in the category of all modules, which will be called large Mod. Based on such study, in addition to the new results, classical results are extended, not only from modules to subcategories but also from small mod to large Mod.
