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 F : C → D is called final if, for any set-valued functor G : D → S e t , the colimit of G is the same as the colimit of G ∘ F . Note that an object d∈Ob(D) is a final object in the usual sense if and only if the functor { ∗ } → d D is a final functor as defined here.

The notion of initial functor is defined as above, replacing final by initial and colimit by limit.