Preservation of quasi-isomorphisms of complexes

Abstract

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〉-1(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 ∈ C ⊏(R) are Y-complexes, then Open image in new window ; Open image in new window . As an application, we give a sufficient condition for the Hom evaluation morphism being invertible.