FI-内射复形

FI-injective complexes

复形范畴中的同调理论是由Cartan和Eilenberg于20世纪50年代引入的,它受到众多学者的关注。由于模的复形可以看成模的推广,因而在复形范畴中也可以开展同调理论的研究。作为FI-内射模的推广,本文定义了FI-内射复形,给出了FI-内射复形与其各个层次上的模之间的联系,利用复形的覆盖刻画了FI-内射复形,最后讨论了FI-内射复形与内射复形之间的关系。

In the 1950 s, Homology theory in the category of complexes was introduced by Cartan and Eilenberg. It has drawn wide attentions from more and more scholars. Since complexes of R-modules can be seen as a generalization of modules,relative homology theory of the category of modules can be generalized to that of complexes. As a generalization of FI-injective module, FI-injective complex is defined. The connection between FI-injective complex and modules of degree n is obtained, for all n in Z. FI-injective complex is discussed through covers. Furthemore, the relation between FP-injective complex and injective complex is given.