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 is called final if, for any set-valued functor , the colimit of G is the same as the colimit of . Note that an object d ∈ Ob(D) is a final object in the usual sense if and only if the functor is a final functor as defined here. The notion of initial functor is defined as above, replacing final by initial and colimit by limit. References . . . See also http://ncatlab.org/nlab/show/final+functor Functors