Indiscrete category

In category theory, a branch of mathematics, an indiscrete category is a category in which there is exactly one morphism between any two objects.

[1] Every class X gives rise to an indiscrete category whose objects are the elements of X such that for any two objects A and B, there is only one morphism from A to B.

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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