|The following examples are "classic" categories. |
- Set - a category of all sets. Its objects are all sets; its morphisms are set functions.
- Setf - a category of all finite sets and functions between them.
- Rel - a category where objects are all sets, and binary relationships play the role of morphisms. Composition is defined via inner join.
- Part - a category of all sets and partial functions as morphisms. A partial function from X to Y is a function from a subset X0 ⊂ X to Y:
- Top - a category of all topological spaces and continuous functions between them.