论文标题
外侧类别的倾斜对
Tilting pairs in extriangulated categories
论文作者
论文摘要
Nakaoka和Palu引入了外部类别，以统一确切类别的属性和三角形类别的扩展子类别。本文介绍了外侧类别中倾斜对的概念。在这种情况下，我们给出了倾斜对的Bazzoni表征。我们还获得了倾斜对的Auslander-Reiten对应关系，这些对应对有限的$ \ MATHCAL {C} $ - 与某些假设的某些自动式子类别$ \ MATHCAL {C C} $的倾斜子类别和某些假设。这概括了WEI和XI给出的已知结果针对ARTIN代数有限生成的模块类别，从而提供了精确和三角形类别的新见解。
Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact categories and extension-closed subcategories of triangulated categories. A notion of tilting pairs in an extriangulated category is introduced in this paper. We give a Bazzoni characterization of tilting pairs in this setting. We also obtain Auslander-Reiten correspondence of tilting pairs which classifies finite $\mathcal{C}$-tilting subcategories for a certain self-orthogonal subcategory $\mathcal{C}$ with some assumptions. This generalizes the known results given by Wei and Xi for the categories of finitely generated modules over Artin algebras, thereby providing new insights in exact and triangulated categories.
