The Idempotent Completion and Costabilization of a Left Trangulated Category

Let (,Ω,Δ) be a left triangulated category.If(■,■,■)denotes the costabilization of the idempotent completion of (,Ω,Δ) and(■,■,■) denotes the idempotent completion of the costabilization of (,Ω,Δ). Then they have the main theorem (■,■,■)≌(■,■,■) as a triangle-equivalence.