论文标题
Gorenstein的外节类别中的物体
Gorenstein Objects in Extriangulated Categories
论文作者
论文摘要
本文主要研究了外侧类别类别中的相对Gorenstein对象$ \ MATHCAL {C} =（\ Mathcal {C}，\ Mathbb {E}，\ Mathfrak {s}）$，带有适当的类$ξ$和这些对象的相关属性。 在第一部分中，我们定义了$ξ$ - $ \ MATHCAL {g} $投影分辨率的概念，并研究$ξ$ -projective解决方案与$ξ$ - $ \ $ \ MATHCAL {G} $投影分辨率分辨率的任何对象$ a $ A $ in $ \ MATHCAL {c} $ a a $ a a a a a a a $ a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a。 $ \ MATHCAL {C}（ - ，\ MATHCAL {p}（ξ））$ - 精确$之一，仅当$ A $具有$ \ MATHCAL {C}（ - ，\ MATHCAL {P}（p}（之一））$ - 精确$ - 精确$ - 精确$ - $之一，$ - 之一 在第二部分中，我们在$ \ Mathcal {c} $中定义了一个特定的$ξ$ -Gorenstein Projective对象，该对象称为$之一，该对象称为$之一 - $ n $ -n $ - stronglongly $ \ nathcal {g} $ph止是projective对象。在此基础上，我们研究$ξ$ - $ m $ -m $ \ mathcal {g} $投影对象和$ξ$ - $ n $ -n $ - stronglongly $ \ mathcal {g} $ Projective对象，只要$ m \ m \ neq n $更重要的是，我们提供了一些$ξ$ - $ n $ -n $ $ \ MATHCAL {G} $ PROFPENTIVE对象的不错的支撑。
This paper mainly studies the relative Gorenstein objects in the extriangulated category $\mathcal{C}=(\mathcal{C},\mathbb{E},\mathfrak{s})$ with a proper class $ξ$ and the related properties of these objects. In the first part, we define the notion of the $ξ$-$\mathcal{G}$projective resolution, and study the relation between $ξ$-projective resolution and $ξ$-$\mathcal{G}$projective resolution for any object $A$ in $\mathcal{C}$, i.e. $A$ has a $\mathcal{C}(-,\mathcal{P}(ξ))$-exact $ξ$-projective resolution if and only if $A$ has a $\mathcal{C}(-,\mathcal{P}(ξ))$-exact $ξ$-$\mathcal{G}$projective resolution. In the second part, we define a particular $ξ$-Gorenstein projective object in $\mathcal{C}$ which called $ξ$-$n$-strongly $\mathcal{G}$projective object. On this basis, we study the relation between $ξ$-$m$-strongly $\mathcal{G}$projective object and $ξ$-$n$-strongly $\mathcal{G}$projective object whenever $m\neq n$, and give some equivalent characterizations of $ξ$-$n$-strongly $\mathcal{G}$projective objects. What is more, we give some nice propsitions of $ξ$-$n$-strongly $\mathcal{G}$projective objects.
