Final functor

In category theory, the notion of final functor is a generalization of the notion of cofinal set from order theory.

A functor ${\displaystyle F:C\to D}$ is called final if, for any set-valued functor ${\displaystyle G:D\to {\textbf {Set}}}$, the colimit of G is the same as the colimit of ${\displaystyle G\circ F}$. The inclusion function of a cofinal subset into a partially ordered set is a final functor.

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