论文标题
遗传性结核对外侧子类别
Hereditary cotorsion pairs on extriangulated subcategories
论文作者
论文摘要
令$ \ Mathcal b $为一个外侧类别，具有足够的投影和足够的注射剂。我们在$ \ Mathcal b $上定义了适当的$ M $ - term子类别$ \ Mathcal g $，这是一个外侧的子类别。然后，我们在$ \ Mathcal g $上的cotorsion对之间进行对应关系，支持$τ$ - 在$ \ Mathcal g $的Abelian商中使用子类别时，当$ \ Mathcal G $时，当$ \ Mathcal g $当$ m = 2 $。如果这种$ \ Mathcal G $是由遗传性的Cotorsion对引起的，那么我们在$ \ Mathcal G $上的CotorSion对与$ \ MATHCAL B $上的中间合并对之间进行对应关系。最后，我们研究了此类外部子类别$ \ MATHCAL G $的重要属性。
Let $\mathcal B$ be an extriangulated category with enough projectives and enough injectives. We define a proper $m$-term subcategory $\mathcal G$ on $\mathcal B$, which is an extriangulated subcategory. Then we give a correspondence between cotorsion pairs on $\mathcal G$, support $τ$-tilting subcategories on an abelian quotient of $\mathcal G$ when $m=2$. If such $\mathcal G$ is induced by a hereditary cotorsion pair, then we give a correspondence between cotorsion pairs on $\mathcal G$ and intermediate cotorsion pairs on $\mathcal B$ under certain assumptions. At last, we study an important property of such extriangulated subcategory $\mathcal G$.
