Indiscrete Category
An indiscrete category is a category (mathematics), category ''C'' in which every hom-set ''C''(''X'', ''Y'') is a singleton (mathematics), singleton. Every class (set theory), 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 equivalence of categories, equivalent to each other. The functor from Set to Cat that sends a set to the corresponding indiscrete category is adjoint functors, right adjoint to the functor that sends a small category to its set of objects. References

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Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. ''Category theory'' is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides an alternative foundation for mathematics to set theory and other proposed axiomatic foundations. In general, the objects and arrows may be abstract entities of any kind, and the ...
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