对偶化范畴的张量积构造  

A construction of dualizing categories by tensor product of categories

作　　者：韩阳[1,2] 张凝鹛 Yang Han;Ningmei Zhang

机构地区：[1]中国科学院数学与系统科学研究院,北京100190 [2]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学：数学》2018年第11期1699-1716,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11571341)资助项目

摘　　要：本文证明了一个局部有限箭图的路范畴模一个单项式容许理想所得的剩余范畴与一个对偶化范畴的张量积的加法包的幂等完备是对偶化的.从而,此张量积范畴的有限表现函子范畴是对偶化的且有几乎可裂序列.作为应用,本文证明了一个对偶化范畴上的有限表现函子范畴的态射范畴与态射合成范畴及各种各样的n-(循环)复形范畴有几乎可裂序列.In this paper, it is shown that, the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo a monomial admissible ideal and a dualizing category, is dualizing. Furthermore, it is proved that the category of finitely presented functors over such a tensor product category is dualizing and has almost split sequences. As applications, the category of morphisms and the category of composable morphisms of the category of finitely presented functors, and the categories of all kinds of n-（cyclic） complexes, over a dualizing category, are proved to have almost split sequences.

关 键 词：对偶化范畴 范畴的张量积 箭图的表示 有限表现函子 几乎可裂序列 

分 类 号：O153.3[理学—数学]