论文标题
切割cotorsion对
Cut cotorsion pairs
论文作者
论文摘要
我们介绍了沿Abelian类别的子类别切割的Cotorsion对的概念。这提供了完整的合并对的概括，并代表了一个限制某些子类别的近似值的一般框架。我们还通过考虑Frobenius Pairs和Auslander-Buchweitz环境的相对类似物，在切割的Cotorsion对与Auslander-Buchweitz近似理论之间表现出一些联系。在相对Gorenstein同源代数，链络合物和准搭换的吊带上的设置中给出了几种应用，同时还可以描述一些重要的结果，这些结果是关于有限尺寸的构想的一些重要成果，静脉子类别的右旁偶置的右伴有右伴有的右旁伴，以及对三角构成类别中的cotorsorsion Pairs类别的描述，如co-sonture co-sonture-sonture-sonture-sonture-sonture-sonture $ sont-$ $ -sont-$ t-t $ t-- $ t- t $ -
We present the concept of cotorsion pairs cut along subcategories of an abelian category. This provides a generalization of complete cotorsion pairs, and represents a general framework to find approximations restricted to certain subcategories. We also exhibit some connections between cut cotorsion pairs and Auslander-Buchweitz approximation theory, by considering relative analogs for Frobenius pairs and Auslander-Buchweitz contexts. Several applications are given in the settings of relative Gorenstein homological algebra, chain complexes and quasi-coherent sheaves, but also to characterize some important results on the Finitistic Dimension Conjecture, the existence of right adjoints of quotient functors by Serre subcategories, and the description of cotorsion pairs in triangulated categories as co-$t$-structures.
