外三角范畴中的相对分解维数

Relative resolution dimensions in extriangulated categories

设■是有足够多投射对象和内射对象的外三角范畴.本文引入相对分解维数、相对余分解维数以及X-完备对和X-遗传对等概念.本文利用X-完备对和X-遗传对刻画对象和子范畴的不同的同调维数与分解维数之间的关系,同时给出X-完备对的心的不同实现.

Let■be an extriangulated category with enough projective and injective objects.We introduce the notions of relative resolution dimensions,relative coresolution dimensions,X-complete pairs and X-hereditary pairs in this paper.Using X-complete pairs and X-hereditary pairs,we describe the relationship between homological dimensions and resolution dimensions of objects and subcategories,respectively,and meanwhile we give some different descriptions for the realization of the hearts of X-complete pairs.