MAGIC009: Category Theory

Course details

A core MAGIC course


Spring 2019
Monday, January 21st to Friday, March 29th


Live lecture hours
Recorded lecture hours
Total advised study hours


11:05 - 11:55


Category theory is the language of much of modern mathematics. It starts from the observation that the collection of all mathematical structures of a certain kind may itself be viewed as a mathematical object - a category.
This is an introductory course in category theory. The main theme will be universal properties in their various manifestations, one of the most important uses of categories in mathematics.


Category theory is an abstract algebraic point of view of mathematics. Some familiarity with an algebraic way of thinking is important. It is therefore an advantage to have studied an undergraduate course in group theory or ring theory, or some other abstract algebra course. I will assume some knowledge of algebra such as vector spaces and their bases, and groups, but a basic undergraduate level knowledge of these subjects is sufficient.


The topics covered are:
  1. Categories
  2. Functors and natural transformations
  3. Adjoints
  4. Limits
  5. Colimits
  6. Interaction between limits and adjoints
  7. Adjoint functor theorems
  8. Representables
  9. Presheaves and the Yoneda lemma
  10. Representables and limits


  • MR

    Prof Michael Rathjen

    University of Leeds


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There are 2 weeks to complete and submit answers online. There are 4 questions. Each question will be marked out of 20. To pass the exam you will need at least 40 points out of the total of 80 points.

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