相对于对偶对的Cartan-Eilenberg复形

Cartan-Eilenberg Complexes Relative to Duality Pairs

设(A,B)是模范畴中的对偶对.首先,引入Cartan-Eilenberg-A复形和Cartan-Eilenberg-B复形的概念;其次,证明(C-E(A),C-E(B))是复形范畴中的对偶对,其中C-E(A),C-E(B)分别表示所有Cartan-Eilenberg-A复形和Cartan-Eilenberg-B复形构成的类;最后,给出对偶对在复形上的应用.

Let(A,B)be a duality pair in the category of modules.Firstly,the concepts of Cartan-Eilenberg-A and Cartan-Eilenberg-B complexes are introduced.Secondly,it is proven that(C-E(A),C-E(B))is a duality pair in the category of complexes,where C-E(A)and C-E(B)denote the class of Cartan-Eilenberg-A complexes and Cartan-Eilenberg-B complexes,respectively.Finally,the application of duality pairs to complexes is given.