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 $$F: C \to D$$ is called final if, for any set-valued functor $$G: D \to \textbf{Set}$$, the colimit of G is the same as the colimit of $$G \circ F$$. Note that an object d ∈ Ob(D) is a final object in the usual sense if and only if the functor $$\{*\} \xrightarrow{d} D$$ is a final functor as defined here.

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