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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.