At the end of lecture 8 you'll now find a proof of the Adjoint Functor Theorem. I also added examples of non-representable functors to lecture 10.



This course is part of the MAGIC core.


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.


Spring 2017 (Monday, January 23 to Friday, March 31)


  • Thu 14:05 - 14:55


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


Michael Rathjen
Phone +44 (0)113 3435109


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Mashaer Alsaeedi
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Floriana Amicone
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Michael Arnold
(East Anglia)
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Thomas Baker
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Carolyn Barker
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Edward Bennett
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John Blackman
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Philip Carter
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Lucas Das Dores
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Lorenzo De Biase
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Liam Dobson
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Paul Druce
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Aeran Fleming
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Christopher Foster
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Ai Guan
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Ben Jones
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Wojciech Porowski
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Giulia Sindoni
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Categories for the working mathematicianMac Lane
Basic Category TheoryLeinster


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The assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be 4 questions. Each question will be marked out of 20. To pass the exam you will need ≥ 40 points out of the total of 80 points.

Exam category theory 2017

Files:Exam paper
Released: Monday 24 April 2017 (118.2 days ago)
Deadline: Sunday 7 May 2017 (104.2 days ago)


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Recorded Lectures

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