sentences:  The theory has been further developed by several other people, including Heller, Franke, Keller and Groth.One of the motivating reasons for considering derivators is the lack of functoriality with the cone construction with triangulated categories.Derivators are able to solve this problem, and solve the inclusion of general homotopy colimits, by keeping track of all possible diagrams in a category with weak equivalences and their relations between each other.