MAGIC009: Category Theory

Course details

A core MAGIC course


Spring 2012
Monday, January 16th to Friday, March 23rd


Live lecture hours
Recorded lecture hours
Total advised study hours


10:05 - 10:55


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.


There are few formal prerequisites to the material. However, I will be giving examples from mathematics to motivate the ideas and demonstrate how they are used, so an undergraduate degree in mathematics (rather than for example computer science or philosophy) would be an advantage. In particular, I will assume some knowledge of algebra such as vector spaces and their bases, and groups, but undergraduate level knowledge of these subjects is sufficient.


The topics covered are:
  1. Categories: definitions, examples, special kinds of arrows and objects, duality
  2. Functors: definitions, examples, full and faithful functors, subcategories, Hom-functors, contravariant functors
  3. Universal properties: examples including vector space bases, fields of fractions, tensor products, quotients, products, and coproducts
  4. Natural transformations: definitions and examples, functor categories, equivalence of categories, horizontal composition
  5. Limits: examples, general definition, computing limits in Set, complete categories
  6. Colimits: definition, examples, computing colimits in Set
  7. Adjunctions: vector space bases, formal definition, examples, unit and counit
  8. Limit preservation: right adjoints preserve limits
  9. Limit creation: general adjoint functor theorem, examples
  10. The category of Sets


  • JK

    Dr Jonathan Kirby

    University of East Anglia


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The assessment for this course will be released on Monday 21st September 2020 and is due in by Friday 13th April 2012 at 23:59.

The course will be assessed by a single exam. The paper is available under the Assignments tab, and the deadline is 13th April 2012.

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


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