Minicourse on Category Theory


at the University of Verona • begin November 10th, 2022 • by Ingo Blechschmidt

Welcome to our joint course on category theory. đź‘‹

The language of category theory has proved to be the lingua franca of diverse subject areas including considerable parts of algebra, geometry, topology, mathematical logic, theoretical computer science and mathematical physics. The strength of category theory is that manifold phenomena can be seen together. As a basic example, category theory reveals a common origin to the commutativity of binary operations such as addition and multiplication of numbers; the cartesian product of sets, groups and spaces; and the pair type in programming. After a gentle introduction into the foundations of category theory, this course will be dedicated to contemporary applications. The course requires no particular prerequisites.

I hope you will enjoy the course. Questions and suggestions are always welcome!

📆 Schedule

    November 2022
Mo Tu We Th Fr Sa Su
    1  2  3  4  5  6
 7  8  9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30

Mondays:    15:30–19:30, Aula B
Wednesdays: 17:30–19:30, Aula C
Thursdays:   9:30–10:30, Aula H
Fridays:    12:30–13:30, Aula C

Tomorrow, on Friday Nov 24th, directly after our final category theory session, there is an extra session on free monads and freer monads in Haskell.

đź’ˇ Syllabus

  1. Categories
  2. Products and coproducts
  3. Functors
  4. Natural transformations
  5. Limits
  6. The Yoneda lemma and adjoints
  7. Monads, monoidal categories and tensor categories
  8. Introduction to quantum field theory
  9. Applications III

Side topic: Sets and classes

  1. Motto and examples
  2. Russell's paradox and its resolution
  3. Proper classes in ZFC
  4. Dealing with size issues
  5. Other set-theoretic phantoms

Side topic: Agda, the programming language, proof language and proof assistant

  1. Basic functions with Booleans and natural numbers
  2. Polymorphic functions and dependent types
  3. Predicates: the Boolean and the witness-based approach
  4. Propositional equality
  5. Proofs with natural numbers
  6. Induction as recursion

đź“– References

đź‘‹ Side topics

đź’¬ Contact

mail: iblech@speicherleck.de
phone: +49 176 95110311 (also Telegram)