论文标题
相对严格的子类别和$τ$ - 利用理论
Relative rigid subcategories and $τ$-tilting theory
论文作者
论文摘要
令$ \ Mathcal b $为一个外侧类别，具有足够的投影$ \ MATHCAL P $和足够的注射剂$ \ Mathcal i $，然后让$ \ Mathcal r $是$ \ MATHCAL B $的违反有限的刚性子类别，其中包含$ \ Mathcal p $。我们有一个Abelian商类别$ \ MATHCAL H/\ MATHCAL R \ subseteq \ Mathcal B/\ Mathcal R $，它是等效的$ {\ rm mod}（\ Mathcal R/\ Mathcal p）$。 In this article, we find a one-to-one correspondence between support $τ$-tilting (resp. $τ$-rigid) subcategories of $\mathcal H/\mathcal R$ and maximal relative rigid (resp. relative rigid) subcategories of $\mathcal H$, and show that support tilting subcategories in $\mathcal H/\mathcal R$ is a special kind of support $τ$ - 使用子类别。我们还研究了$ \ Mathcal B/\ Mathcal R $的倾斜子类别与$ \ Mathcal B $的集群倾斜子类别之间的关系，当$ \ Mathcal r $是集群倾斜时。
Let $\mathcal B$ be an extriangulated category with enough projectives $\mathcal P$ and enough injectives $\mathcal I$, and let $\mathcal R$ be a contravariantly finite rigid subcategory of $\mathcal B$ which contains $\mathcal P$. We have an abelian quotient category $\mathcal H/\mathcal R\subseteq \mathcal B/\mathcal R$ which is equivalent ${\rm mod}(\mathcal R/\mathcal P)$. In this article, we find a one-to-one correspondence between support $τ$-tilting (resp. $τ$-rigid) subcategories of $\mathcal H/\mathcal R$ and maximal relative rigid (resp. relative rigid) subcategories of $\mathcal H$, and show that support tilting subcategories in $\mathcal H/\mathcal R$ is a special kind of support $τ$-tilting subcategories. We also study the relation between tilting subcategories of $\mathcal B/\mathcal R$ and cluster tilting subcategories of $\mathcal B$ when $\mathcal R$ is cluster tilting.
