CPSC 617: Category Theory for Computer
Lecturer: Robin Cockett
Most of the following topics will be covered:
- Introduction to categories: definitions and examples.
- Properties of maps: monic, epic, section, retraction,
idempotent, isomorphism, factorization.
- Functors and natural transformations: the category of
categories, Yoneda lemma.
- Adjoints and monads.
- Limits and colimits.
- Cartesian closed categories.
- Inductive and coinductive data types.
- Introduction to monoidal categories.
- Introduction to fibrations.
There are many good texts introducing category
- Category for Computer Science, Micheal Barr and
Charles Wells (available on line) 1999
- Category Theory, Steve Awodey, Oxford University
- Categories for the working mathematician, Saunders
Mac Lane, Springer Verlag 2000.
- Introduction to higher-order categorical logic,
Joachim Lambek and Phil Scott 1988.
- Basic Category Theory for computer scientists,
Benjamin Pierce, MIT press, 1991.
- Categories for Types, Roy Crole, Cambridge University
- Practical Foundations of Mathematics, Paul Taylor,
Cambridge University Press, 1999
There will be four exercises sets ...
- Here is the first.
- Here is the second.
- Here is the third.
- Here is the
- My course notes are here. I do
update them from time to time! ... comments are welcome.
- An electronic Journal: Theory and Applications of Categories (TAC).
- Daniele Turi's Category Theory notes here.
- Notes from Barr and Wells here.
- Maarten Fokkinga's gentle introduction here.
- Japp van Oosten's notes on basic category theory here.
- Catch it all on youtube here.
Links to the 2008 project papers: Aaron,
Links to the 2009 project papers: Jonathan,
Links to 2010 project papers: Masuka,