sentences:  Heuristcally, given the diagramformula_1which is a category with two objects and one non-identity arrow and a functorformula_2to a category formula_3 with a class of weak-equivalences formula_4, and satisfying the right hypotheses, should have an associated functorformula_5where the target object is unique upto weak equivalence in formula_6.Derivators are able to encode this kind of information and provide a diagram calculus to use in derived categories and homotopy theory.Formally, a prederivator formula_7 is a 2-functorformula_8from a suitable 2-category of indices to the category of categories.