论文标题
外侧类别中完整的共同体学平衡
Balance of complete cohomology in extriangulated categories
论文作者
论文摘要
令$（\ Mathcal {C}，\ Mathbb {e}，\ Mathfrak {s}）$为一个外部缝制类别，具有适当的类$之一的$ \ Mathbb {e} $ - 三角形。在本文中，我们研究了$（\ mathcal {c}，\ mathbb {e}，\ mathfrak {s}）$中完整的共同体学的平衡，这是由于nucinkis的结果是，模块的完整共同体学在绝对共同体学上无法平衡。作为应用程序，我们提供了一些标准，以识别三角策略，将其视为Gorenstein，而Artin代数为$ f $ -Gorenstein。
Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles. In this paper, we study the balance of complete cohomology in $(\mathcal{C},\mathbb{E},\mathfrak{s})$, which is motivated by a result of Nucinkis that complete cohomology of modules is not balanced in the way the absolute cohomology Ext is balanced. As an application, we give some criteria for identifying a triangulated catgory to be Gorenstein and an artin algebra to be $F$-Gorenstein.
