Final functor

Summary

A final functor $F \colon \mathcal{C} \to \mathcal{D}$ is a functor such that restricting a diagram on $\mathcal{D}$ along $F$ does not change its colimit. It is the categorical form of a cofinal subset of a directed set, as in cofinality. Final functors let one compute a colimit over a smaller or simpler index category. Some authors call them cofinal functors; the dual notion is an initial functor.