# Category theory

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Michael Barr and Charles Wells: [http://www.cwru.edu/artsci/math/wells/pub/ttt.html Toposes, Triples and Theories]. The online free available book is both an introductory and a detailed description of category theory. By the way, it is also a category theoretical descripton of the concept of ''monad'' (the book uses another name instead of monad: ''triple''). | Michael Barr and Charles Wells: [http://www.cwru.edu/artsci/math/wells/pub/ttt.html Toposes, Triples and Theories]. The online free available book is both an introductory and a detailed description of category theory. By the way, it is also a category theoretical descripton of the concept of ''monad'' (the book uses another name instead of monad: ''triple''). | ||

+ | HaWiki's [http://www.haskell.org/hawiki/CategoryTheory CategoryTheory] is also a good theoretical introduction, and besides that, it explains how concepts of category theory are important in Haskell programming. | ||

+ | [http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html A Gentle Introduction to Category Theory - the calculational approach] written by [http://wwwhome.cs.utwente.nl/~fokkinga/index.html Maarten M Fokkinga]. | ||

== Categorical programming == | == Categorical programming == |

## Revision as of 19:50, 11 June 2006

## Contents |

## 1 Foundations

Michael Barr and Charles Wells: Toposes, Triples and Theories. The online free available book is both an introductory and a detailed description of category theory. By the way, it is also a category theoretical descripton of the concept of *monad* (the book uses another name instead of monad: *triple*).

HaWiki's CategoryTheory is also a good theoretical introduction, and besides that, it explains how concepts of category theory are important in Haskell programming.

A Gentle Introduction to Category Theory - the calculational approach written by Maarten M Fokkinga.

## 2 Categorical programming

Catamorphisms and related concepts, categorical approach to functional programming, categorical programming. Many materials cited here refer to category theory, so as an introduction to this discipline see the #Foundations section.

- Erik Meijer, Maarten Fokkinga, Ross Paterson: Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire. See also related documents (in the CiteSeer page). Understanding the article does not require a category theory knowledge -- a self-contained material on the concept of catamorphism, anamoprhism and other related concepts.
- Varmo Vene and Tarmo Uustalu: Functional Programming with Apomorphisms / Corecursion
- Varmo Vene: Categorical Programming with Inductive and Coinductive Types. The book accompanies the deep categorical theory topic with Haskell examples.
- Tatsuya Hagino: A Categorical Programming Language
- Charity, a categorical programming language implementation.
- Deeply uncurried products, as categorists might like them article mentions a conjecture: relatedness to Combinatory logic