Indiscrete category

An indiscrete category is a category "C" in which every hom-set "C"("X", "Y") is a singleton. Every class "X" gives rise to an indiscrete category whose objects are the elements of "X" with exactly one morphism between any two objects. Any two nonempty indiscrete categories are equivalent to each other. The functor from Set to Cat that sends a set to the corresponding indiscrete category is right adjoint to the functor that sends a small category to its set of objects.