Four different categories are introduced which could serve as
basic categories for construction of Kuratowski closure and
interior operators on the set of Q-valued fuzzy sets,
F-transforms of Q-valued fuzzy sets with respect to fuzzy
partitions and fuzzy approximation spaces, respectively. Some
relationships among these notions are investigated in a form
of functors between categories, commutative diagrams of these
functors and natural transformation between these functors.