标题： 余倾斜复形与AIR-余倾斜模 显示英文标题

标题： Cosilting complexes and AIR-cotilting modules

摘要： 我们引入并研究了余倾斜复形、余倾斜模和AIR-余倾斜模这三个新概念。我们证明了与倾斜模的对偶情况不同，AIR-余倾斜模、余倾斜模和拟余倾斜模这三者是等价的。进一步地，我们展示了以下四类对象之间存在双射：（1）AIR-余倾斜模（相应地，余倾斜模、拟余倾斜模）的等价类；（2）2-项余倾斜复形的等价类；（3）挠自由覆盖类；（4）挠自由特殊先覆盖类。此外，我们将Auslander和Reiten关于某些协变有限子范畴与余倾斜模之间对应关系的经典结果推广到了余倾斜复形的情形。 显示英文摘要

摘要： We introduce and study the new concepts of cosilting complexes, cosilting modules and AIR-cotilting modules. We prove that the three concepts AIR-cotilting modules, cosilting modules and quasi-cotilting modules coincide with each other, in contrast with the dual fact that AIR-tilting modules, silting modules and quasi-tilting modules are different. Further, we show that there are bijections between the following four classes (1) equivalent classes of AIR-cotilting (resp., cosilting, quasi-cotilting) modules, (2) equivalent classes of 2-term cosilting complexes, (3) torsion-free cover classes and (4) torsion-free special precover classes. We also extend a classical result of Auslander and Reiten on the correspondence between certain contravariantly finite subcategories and cotilting modules to the case of cosilting complexes.