论文标题
Avramov-Martsinkovsky类型的外侧类别的精确序列
Avramov-Martsinkovsky type exact sequences for 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，我们首先以$ξ$ - $ \ $ \ MATHCAL {G} $投影分辨率和$ξ$ - $ \ MATHCAL {G} $ Injextive Coresolutions，分别介绍$ξ$ -Gorenstein共同体学，然后我们获得$ -GorenStein Cohomology的余额。此外，我们研究了$ξ$ - 生物学之间的相互作用，$ξ$ -Gorenstein的共同体和$ξ$ -Complete Cromology，并在此设置中获得Avramov-Martsinkovsky类型的精确序列。
Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles. In this paper, we first introduce the $ξ$-Gorenstein cohomology in terms of $ξ$-$\mathcal{G}$projective resolutions and $ξ$-$\mathcal{G}$injective coresolutions, respectively, and then we get the balance of $ξ$-Gorenstein cohomology. Moreover, we study the interplay among $ξ$-cohomology, $ξ$-Gorenstein cohomology and $ξ$-complete cohomology, and obtain the Avramov-Martsinkovsky type exact sequences in this setting.
