> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/450-category-theory/10-categories/named-categories.md).

# Index of named categories

𝗦𝗲𝘁 𝗥𝗲𝗹 𝗚𝗿 𝗚𝗿𝗽 𝗛𝗮𝘀𝗸 𝗧𝗼𝗽 𝗩𝗲𝗰𝘁 𝗖𝗮𝘁

Classification

* *Monoids* are categories with a single object.

Named

* `𝗦𝗲𝘁` category of (small) sets and functions
* `𝗥𝗲𝗹` category of sets and relations
* `𝗣𝗿𝗲𝗼𝗿𝗱` category of preorders and order preserving maps
* `𝗖𝗣𝗢` category of complete partial orders and continuous functions
* `𝗠𝗼𝗻` category of monoids and monoid morphisms
* `𝗚𝗿𝗽` category of groups and group morphisms
* `𝗥𝗻𝗴` category of rings and ring morphisms
* `𝗚𝗿` category of directed graphs with vertices and edges, paths
* `𝗚𝗿𝗽𝗵` category of graphs and graph morphisms
* `𝗧𝗼𝗽` category of topological spaces and continuous maps
* `𝗩𝗲𝗰𝘁` category of vector spaces and linear transformations
* `𝗛𝗮𝘀𝗸` category of Haskell types and Haskell functions

Hierarchy

* `𝗖𝗮𝘁` category with categories as objects and functors as arrows
* `𝗖𝗮𝘁-2` category of categories
* `n𝗖𝗮𝘁` category of categories

Unnamed

* category of data types and functions on data structures
* category of functions and data flows (approx. data flow diagram)
* category of stateful objects and dependencies (approx. object diagram)
* category of values and value constructors
* category of states and messages (approx. state diagram)

The category of small categories, Cat, is a category with categories as objects and functors as morphisms between categories.