Preservation of Quasi-isomorphisms of Complexes  

作　　者：Zhong Kui LIU 

机构地区：[1]Department of Mathematics,Northwest Normal University

出　　处：《Acta Mathematica Sinica,English Series》2012年第12期2489-2500,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10961021);Program of Science and Technique of Gansu Province (Grant No. 1010RJZA025)

摘　　要：We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext〉I（X,Y） = 0 for each object X ∈ X and each object Y ∈ Y. We show that if A,B ∈ C^（R） are X-complexes and U, V ∈ Cr（R） are Y-complexes, then U V Hom（A, U） Hom（A, Y）; A B Hom（B, U） Hom（A, U）. As an application, we give a sufficient condition for the Hom evaluation morphism being invertible.We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext〉I（X,Y） = 0 for each object X ∈ X and each object Y ∈ Y. We show that if A,B ∈ C^（R） are X-complexes and U, V ∈ Cr（R） are Y-complexes, then U V Hom（A, U） Hom（A, Y）; A B Hom（B, U） Hom（A, U）. As an application, we give a sufficient condition for the Hom evaluation morphism being invertible.

关 键 词：Quasi-isomorphism equivalence derived functor Gorenstein homological dimension Hom evaluation morphism 

分 类 号：O153.3[理学—数学]