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.