Lecturer: Robin Cockett

COURSE OUTLINE:
     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 theory (it is worth having one at hand!):

1. Category for Computer Science, Micheal Barr and Charles Wells (available on line) 1999
2. Category Theory, Steve Awodey, Oxford University Press 2006 (second edition 2010).
3. Categories for the working mathematician, Saunders Mac Lane, Springer Verlag 2000.
4. Introduction to higher-order categorical logic, Joachim Lambek and Phil Scott 1988.
5. Basic Category Theory for computer scientists, Benjamin Pierce, MIT press, 1991.
6. Categories for Types, Roy Crole, Cambridge University Press,1993.
7. Practical Foundations of Mathematics, Paul Taylor, Cambridge University Press, 1999
8. Basic Category Theory, Tom Leister, Cambridge University Press, 2014
9. Category Theory in Context,  Emily Reil, Dover Modern Math Originals, 2016
   
10.  .......
    

There will be four exercises sets (80%)

1. Here is the first (due January 26th 2024, worth 20%).
2. Here is the second (due February 16th 2024, worth 20%)
   
3. Here is the third (due March 29st 2023, worth 20%)
   
4. Here  is the fourth (due April 9th 2024, worth 20%)
   

There will be a final project (worth 20%) which should be a study of some topic in an area related to category theory.  You are expected to present your projects and to provide a write up of about 15-20 pages.

• 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.