- News: On December 10th, 2007 we created a wiki/blog for the new seminar series, Categories Logic and Foundations of Physics (link). We also have a facebook group.
The theory of categories has come to occupy a central position in contemporary mathematics and theoretical computer science, and in particular, mathematical physics. Category theory naturally arises when faced with developing new mathematics and new logics and is also crucial in understanding existing structures.
- Category theory online video collection (Catsters youtube channel)
- What is a category?
- List of category theory topics
- Glossary of category theory
- Categories mailing list
Online textbooks:
- Categories, Types and Structures. An introduction to Category Theory for the working computer scientist, Andrea Asperti and Giuseppe Longo.
- A Categorical Primer.
- A gentle introduction to category theory, Maarten M. Fokkinga.
- An introduction to the theory of categories, David Madore.
- This is a list of Peter Selinger's papers, along with abstracts and hyperlinks.
Linear Logic
In mathematical logic, linear logic is a type of 'resource sensitive' logic that has interesting ties to the theory of computation and category theory. It borrows some ideas from Modal Logic in order to better express propositional logics.
Online Books/papers:
- Introduction to Linear Logic
- Girard, Jean-Yves. Linear logic, Theoretical Computer Science, London Mathematical 50:1, pp. 1-102, 1987.
- Linear logic its syntax and semantics
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Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the context of
Functorial Semantics of Algebraic Theories, F. William Lawvere. - Patrick Lincoln has an Introduction to Linear Logic
- Introduction to Linear Logic by Torben Brauner
- A taste of linear logic by Philip Wadler
- Linear Logic, Roberto Di Cosmo] and Dale Miller.
- Category theory for beginners
- category theory for linear logicians
- Proofs and Types
- Categorical Logic lecture notes by Steve Awodey.
- Practical Foundations of Mathematics, by Paul Taylor, Cambridge University Press.
- Conceptual Mathematics --- basic course covering a range of elementary mathematics including some basic Category theory. (see also Space and Spacetime)
Here is a list of categories leading up to the Dagger compact category which was used to recast the standard axiomatization of quantum mechanics in a category theoretic context. First, here are some good introductions to quantum information theory cast in a categorical framework:
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S. Abramsky and B. Coecke, A categorical semantics of quantum protocols, Proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS'04). IEEE Computer Science Press (2004).
See also these papers by B. Coecke: - Kindergarten Quantum Mechanics
- Introducing categories to the practicing physicist
Products, Pullbacks and Pushouts are critically important concepts in the theory of categories.
- Monoidal (or tensor) category
- A symmetric monoidal category is a Braided monoidal category with a specific braid rule---see also: Baez week137
- Dagger category
- Closed category
- Compact closed category---see also Traced monoidal category
- Dagger symmetric monoidal category
- Dagger compact category
Groups working on category theory
LaTeX
- Paul Taylor's Commutative Diagrams in TeX, for which a commonly-used alternative is xymatrix.
- LaTeX for logicians
Journals/Papers
- Theory and Applications of Categories---open access journal.
- Mathematical Structures in Computer Science
- List of important publications in mathematics
- Journal of Mathematical Physics
Other
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CCS1a: Categories, Proofs and Processes (Courses I took Michaelmas 2007)
Dr Tzevelekos (internal course materials link)
M,Th.3 (weeks 1-8), M.4 (weeks 5-8)
Computing Laboratory
- Category Theory Demos these generate examples, with diagrams, of concepts in category theory --- by Jocelyn Paine.
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Interesting book: Conceptual Mathematics: A First Introduction to Categories
By F. W. Lawvere and Stephen Hoel Schanuel. (Here I link 2 a number of pages free online)
Domain Theory
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A standard resource on domain theory, which is freely available online:
S. Abramsky and A. Jung (1994). "Domain theory" (PDF), Handbook of Logic in Computer Science III, Oxford University Press. ISBN 0-19-853762-X.
