COSILTING复合体和AIR-cotilting模块
Cosilting complexes and AIR-cotilting modules
摘要：
介绍并研究了共淤复合体、共淤模块和AIR共倾模块的新概念。我们证明了AIR-共倾模、共淤模和拟共倾模这三个概念是一致的，而AIR-倾模、共淤模和拟倾模是不同的这一双重事实则相反。进一步，我们证明了在以下四类（1）等价的AIR-共倾类（分别为，（2）2-term cosilting复形的等价类，（3）无挠覆盖类和（4）无挠特殊precover类。我们还将Auslander和Reiten关于某些逆变有限子范畴与cotilting模之间的对应关系的经典结果推广到cosilting复形的情形。
英文摘要：
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.
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