Final functor

In category theory, the notion of "final functor" (resp. "initial functor") is a generalization of the notion of final object (resp. initial object) in a category.
A functor formula_1 is called "final" if, for any set-valued functor formula_2, the colimit of "G" is the same as the colimit of formula_3. Note that an object "d" ∈ Ob("D") is a final object in the usual sense if and only if the functor formula_4 is a final functor as defined here.
The notion of "initial functor" is defined as above, replacing "final" by "initial" and "colimit" by "limit".