Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions
Lili Shen, Dexue Zhang · Theory and applications of categories · 2013
Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads.These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory.It is proved that these two processes are functorial with infomorphisms playing as morphisms between distributors; and that the free cocompletion functor of Q-categories factors through both of these functors.This work is supported by Natural