Examples of Categories
The following examples are "classic" categories.
  1. Set - a category of all sets. Its objects are all sets; its morphisms are set functions.
  2. Setf - a category of all finite sets and functions between them.
  3. Rel - a category where objects are all sets, and binary relationships play the role of morphisms. Composition is defined via inner join.
  4. 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:
       X0 X
  5. Top - a category of all topological spaces and continuous functions between them.