论文标题
三角策式类别的Abelian类别通过Nakaoka-Palu的本地化
Abelian categories from triangulated categories via Nakaoka-Palu's localization
论文作者
论文摘要
本文的目的是为Abe-Nakaoka的心脏结构扩展，以下对模块类别的以下两个不同的实现在三角形类别中的刚性物体的内态戒指：Buan-Marsh的本地化和Iyama-Yoshino的亚基。我们的方法取决于对Nakaoka-Palu的HTCP定位的修改，这是对外部类别的Gabriel-Zisman定位，这也被认为是原始类别的子因子。除了心脏结构之外，我们广义的HTCP定位涉及以下现象：（1）相对于一类对象的稳定类别； （2）回忆三角类别； （3）在轻度假设下回忆阿贝尔类别。
The aim of this paper is to provide an expansion to Abe-Nakaoka's heart construction of the following two different realizations of the module category over the endomorphism ring of a rigid object in a triangulated category: Buan-Marsh's localization and Iyama-Yoshino's subfactor. Our method depends on a modification of Nakaoka-Palu's HTCP localization, a Gabriel-Zisman localization of extriangulated categories which is also realized as a subfactor of the original ones. Besides of the heart construction, our generalized HTCP localization involves the following phenomena: (1) stable category with respect to a class of objects; (2) recollement of triangulated categories; (3) recollement of abelian categories under a mild assumption.
