Definitions Transfors between 2-categories Morphisms in 2-categories Structures in 2-categories Limits in 2-categories Structures on 2-categories The Kan extension of a functor with respect to a functor is, if it exists, a kind of best approximation to the problem of finding a functor such that hence to extending the domain of through from to . More generally, this notion makes sense not only in Cat but in any 2-category. Similarly, a Kan lift is the best approximation to lifting a morphism...