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.[1]

References

Crole, Roy L. (1993). Categories for Types. Cambridge University Press. p. 83. ISBN 9780521457019. Retrieved February 3, 2024 – via Google Books.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[auto-1] Crole, Roy L. (1993). Categories for Types. Cambridge University Press. p. 83. ISBN 9780521457019. Retrieved February 3, 2024 – via Google Books.