Category theory

at MGS 2021.

This course introduces the basics of category theory. I will cover:

  • categories, duality and functors,
  • products, coproducts, exponentials and cartesian closed categories,
  • natural transformations, equivalences and adjunctions.

If time allows I will cover also monads and their algebras. Each of these topics will be illustrated with several examples from mathematics and computer science.

Our main reference is S. Awodey, Category theory, 2nd edition, Oxford Logic Guides 52.

Further readings (feedbacks on this list are welcome!):

  • S. Mac Lane, Categories for the working mathematician. (The classic one. It is what the title says.)
  • E. Riehl, Category theory in context. (Geared towards mathematicians, but it’s a beautiful book in my opinion so you might want to give it a try.)
  • T. Leinster, Basic category theory. (Only the essential stuff, but with little prerequisites.)
  • M. Barr and C. Wells, Category theory for computing science. (Graphs have a prominent role.)
  • B. Milewski, Category theory for programmers. (From the preface: “[…] targeted at programmers. Mind you, not computer scientists but programmers — engineers rather than scientists.” But I can’t comment since I have not read it.)
  • R.M. Burstall and D. Rydeheard, Computational category theory. (Suggested by a participant. Again, can’t comment since I have not read it.)

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