Triangulated equivalence between a homotopy category and a triangulated quotient category

Relative global dimensions and stable homotopy categories

“…Conversely, we let X ∈ D b (R) (X is also an object of D b (R)/K b (Prj)). By (iii) and [13,Cor. 5.9], the functor…”

“…(ii) =⇒ (iii). From a result by Di, Liu, Yang and Zhang [13,Cor. 5.9], the induced natural functor F : GPac → D b (R) GPac /K b (Prj) is a triangulated equivalence, so the statement (iii) follows from (ii).…”