Category theory

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).

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