Introduction
Category
Examples of Categories
More Examples
Extra Material
Functor
Examples of Functors
More Examples
Natural Transformation
Examples
More Examples
Monad
Monad Examples
More Examples
Exception Monad
State Machine Monad
State Machine (cont'd)
Monads in Programming
References
Haskell IO |
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.
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