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 objec...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.展开更多
基金Supported by National Natural Science Foundation of China (Grant No. 10961021)Program of Science and Technique of Gansu Province (Grant No. 1010RJZA025)
文摘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.
