MAGIC009: Category Theory

Course details

A core MAGIC course


Autumn 2021
Monday, October 4th to Friday, December 10th


Live lecture hours
Recorded lecture hours
Total advised study hours


10:05 - 10:55 (UK)


Category theory begins with the observation that the collection of mathematical objects of a given kind (groups, topological spaces, graphs, etc...) together with the appropriate mappings between them (group homomorphism, continuous function, graph morphism) is an interesting mathematical structure in its own right: a category. 

Category theory, i.e. the study of categories, provides tools that can be applied uniformly to different kinds of mathematical structures and a convenient language to relate them precisely. This course will be an introduction to category theory. The main theme will be universal properties in their various manifestations, which is one of the most important uses of category theory in mathematics. Apart from introducing specific concepts and presenting the key results, one of the goals of the module is to teach you how to reason categorically.


It will be useful to have taken an undergraduate course in group theory or commutative algebra or some other abstract algebra course.

I will try to illustrate notions with examples from different areas, but you may find it useful to come up with examples from your preferred areas. 


  • Categories and functors. 
  • Universal arrows. 
  • Natural transformations and functor categories. 
  • Colimits. 
  • Duality and limits. 
  • Adjunctions. 
  • Preservation of limits. 
  • Presheaves and the Yoneda lemma.
  • Representables and limits
  • Kan extensions.


  • MR

    Professor Michael Rathjen

    University of Leeds


No bibliography has been specified for this course.


The assessment for this course will be released on Monday 10th January 2022 at 00:00 and is due in before Sunday 23rd January 2022 at 23:59.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.


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