sentences:  In the motivating example, this is just precompositition, so given a functor formula_15 there is an associated functor formula_16.Note these 2-functors could be taken to beformula_17where formula_4 is a suitable class of weak equivalences in a category formula_3.There are a number of examples of indexing categories used in this construction
  
  
  Derivators are then the axiomatization of prederivators which come equipped with adjoint functorsformula_25where formula_26 is left adjoint to formula_13 and so on.