**Lecturer: Robin Cockett**

**COURSE OUTLINE:
** Here.
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 aremanygood texts introducing category theory:

Category for Computer Science, Micheal Barr and Charles Wells (available on line) 1999Category Theory, Steve Awodey, Oxford University Press 2006.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 Press,1993.Practical Foundations of Mathematics, Paul Taylor, Cambridge University Press, 1999- .......

Exercises:

There will be four exercises sets ...

- 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, Kevin, Robert, Sarah!

Links to the 2009 project papers: Jonathan, Mark!

Links to 2010 project papers: Masuka, Subashis!