Indiscrete category: Difference between revisions
Content deleted Content added
Was wrong as stated. There are two morphisms between any two objects. There is one morphism going from A to B and one the other way around. |
Added source (WP:FEB24). |
||
| Line 1: | Line 1: | ||
{{ |
{{more citations needed|date=February 2024}} |
||
In [[category theory]], a branch of [[mathematics]], an '''indiscrete category''' is a [[category (mathematics)|category]] in which there is exactly one [[morphism]] between any two objects.<ref>https://www.google.com/books/edition/Categories_for_Types/mHptq6sqJRIC?hl=en&gbpv=1&dq=%22indiscrete+category%22+%22adjoint%22&pg=PA83&printsec=frontcover</ref> 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.<ref>https://www.google.com/books/edition/Categories_for_Types/mHptq6sqJRIC?hl=en&gbpv=1&dq=%22indiscrete+category%22+%22adjoint%22&pg=PA83&printsec=frontcover</ref> |
|||
==References== |
==References== |
||
{{reflist}} |
{{reflist}} |
||
{{categorytheory-stub}} |
{{categorytheory-stub}} |
||
[[Category:Category theory]] |
[[Category:Category theory]] |
||
Revision as of 00:01, 3 February 2024
 | This article needs additional citations for verification. (February 2024) |
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.[2]
References
- ^ https://www.google.com/books/edition/Categories_for_Types/mHptq6sqJRIC?hl=en&gbpv=1&dq=%22indiscrete+category%22+%22adjoint%22&pg=PA83&printsec=frontcover
- ^ https://www.google.com/books/edition/Categories_for_Types/mHptq6sqJRIC?hl=en&gbpv=1&dq=%22indiscrete+category%22+%22adjoint%22&pg=PA83&printsec=frontcover
 | This category theory-related article is a stub. You can help Wikipedia by expanding it. |