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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.
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