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In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense". Categories appear in most branches of mathematics, in some areas of theoretical computer science and mathematical physics, and have been a unifying notion. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1945, in connection with algebraic topology.

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The study of categories is an attempt to capture what is commonly found in various classes of related mathematical structures.

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Ccard :: Special Decks
Logic and Foundations :: Math
Algebraic Topology :: Topology

 
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A Gentle Introduction to Category Theory - Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particular adjunctions. Proofs are given in a calculational style, and the (few) examples are taken from algorithmics. The text is a long PostScript file.

Categorical Myths and Legends - An archive of stories about category theorists.

Categories Home Page - Web page for the category theory mailing list.

Categories, Quantization, and Much More - Introductory article by John Baez.

Category Theory - This expository article is an entry in the Stanford Encyclopedia of Philosophy.

Category Theory and Homological Algebra - In the known maths series.

500 Computational Category Theory - An implementation of concepts and constructions from category theory in the functional programming language Standard ML. Documentation and code.
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CT Category Theory - Section of the e-print arXiv dealing with category theory, including such topics as: enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

Descent and Category Theory Connections - Maintained by M. Alsani.

Groupoid Home Page - Maintained by Birant Ramazan. Address book, open problems, meetings, pictures, other resources.

Groupoids - Notes by Ronald Brown.

Higher-Dimensional Categories - An illustrated guide book by Eugenia Cheng and Aaron Lauda (PS/PDF).

Open Problems on Model Categories - Problems on model categories listed by Mark Hovey at Wesleyan University.
Meta Description: [ Problems on model categories, listed by Mark Hovey, mathematician at Wesleyan University ]

Paul Taylor's Home Page - Includes papers on category theory.

500 Structures Directory - Email directory of logicians, algebraists, and programming linguists working primarily on structural problems in mathematics and computer science.

The Computational Category Theory Project - The aim of the project is the development of software on a wide variety of platforms for computing with mathematical categories and associated algebraic structures.

Toposes, Triples and Theories - By Michael Barr and Charles Wells, 1983. A revised and corrected version is now available free for downloading. Formats: DVI, PDF, PostScript.

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