sentences:  Typically such 2-functors come from considering the categories formula_9 where formula_3 is called the category of coefficients.For example, formula_11 could be the category of small categories which are filtered, whose objects can be thought of as the indexing sets for a filtered colimit.Then, given a morphism of diagramsformula_12denote formula_13 byformula_14This is called the inverse image functor.