| As a bridge between module categories and derived categories,categories of complexes are extremely important.Currently,the research on homological properties of objects in categories has not been fully developed,and there are a lot of problems to be solved.As a new field,representation theory of infinite categories has attracted great attention of mathematicians:In this paper,the representation theory of infinite categories is used to investigate categories the complexes,and to obtain representation theoretic and homological properties of them.We classify simple objects and projective objects.We study projective dimensions of finitely generated complexes,and classify all finitely generated complexes with finite projective dimensions. |
PDF Full Text Request