Let be an extriangulated category with enough projectives \(\mathcal P\) and enough injectives \(\mathcal I\), and let be a contravariantly finite rigid subcategory of which contains \(\mathcal P\). We have an abelian quotient category \(\\mathcal{H} / \mathcal{R} \subseteq / \mathcal{B} / \mathcal{R} \) which is equivalent to \(\mod (\mathcal{R} / \mathcal{P})\). In this article, we find a one-to-one correspondence between support τ-tilting (resp. τ-rigid) subcategories of / and maximal relative rigid (resp. relative rigid) subcategories of , and show that support tilting subcategories in / is a special kind of support τ-tilting subcategories. We also study the relation between tilting subcategories of / and cluster tilting subcategories of when is cluster tilting.

让是一个具有足够射影\(\mathcal P\)和足够单射\(\mathcal I\)的外三角化类别，并让其成为包含\(\mathcal P\)的逆变有限刚性子类别。我们有一个阿贝尔商范畴\(\\mathcal{H} / \mathcal{R} \subseteq / \mathcal{B} / \mathcal{R} \)等价于\(\mod (\mathcal{R} / \mathcal{P})\)。在本文中，我们发现 / 的支撑τ -tilting (resp. τ -rigid) 子类别与 的最大相对刚性 (resp.relativerigid) 子类别之间存在一一对应关系，并表明 / 中的支撑倾斜子类别是一种特殊的支持τ- 倾斜子类别。我们还研究了 / 的倾斜子类别与集群倾斜时的集群倾斜子类别之间的关系。