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This course is part of the MAGIC core.


Category theory provides a convenient and powerful language that can be used in a variety of areas, including algebra, algebraic geometry, algebraic topology, mathematical logic and mathematical physics. The subject begins with the observation that all mathematical structures of a given kind (groups, topological spaces, etc..) and their associated morphisms (group homomorphisms, continuous functions, ...) can be assembled naturally into new kind of mathematical structure, a category. Because of this, category theory provides tools that can be applied uniformly in different fields.

This module 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, one of the goals of the module is to show how to think categorically.


Autumn 2020 (Monday, October 5 to Friday, December 11)


  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40


  • Fri 10:05 - 10:55


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.


The topics covered are:
  1. Categories and functors.
  2. Initial objects and comma categories.
  3. Universal arrows.
  4. Natural transformations and functor categories.
  5. Colimits.
  6. Duality and limits.
  7. Adjunctions.
  8. Preservation of limits.
  9. Presheaves and the Yoneda lemma
  10. Representables and limits


Nicola Gambino
Phone +44 (0)113 3435143
Photo of Nicola Gambino


Categories for the working mathematicianMac Lane
Basic Category TheoryLeinster


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Recorded Lectures

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