... spaces are finitely generated over R. For an R-module M , we write SuppRM = {p ∈ SpecR |Mp 6= 0}. The following theorem can be used to explain results on the symmetry of Hom vanishing, as studied in =-=[1, 6]-=-. Theorem 7.6. Let X and Y be objects in T. (1) If Hom∗T(X,Y ) is finitely generated over R, then SuppR Hom ∗ T(X,Y ) ⊆ (suppRX) ∩ (suppR Y ). (2) If T is stratified by the action of R, then SuppR Hom...