Alexander Kurz

Graduate teaching

(under construction)

I am always happy to talk about category theory. If you are interested in category theory feel free to get in touch. Here are some notes that I have been using for teaching category theory in the past.

Recent Notes

In this section, I collect notes that I used more recently and intend to update and maintain.

• A Very Short Introduction to Monads.
• A very short introduction to Category Theory as an Axiomatic Theory of Structure. This
  • is lecture 3 of a Short Introduction to Monads but can be read independently if you ignore some references to the earlier lectures.
  • also contains a list of online books with introductions to category theory.

Older Notes

In this section I collect notes that may still be usefull as introductions and for background information.

• Coalgebras and Modal Logic. ESSLLI, Helsinki 2001.

• Slides on Coinduction.

• An Introduction to Stone Duality. MGS 2004.

• Topics in Coalgebra. Copenhagen 2004.

• Coalgebras and Their Logics. Logic Colummn, 2006.

• Modal Logics are Coalgebraic with Cirstea, Pattinson, Schröder, Venema. BCS, 2008.

• A Short Introduction to Quantale Enriched Categories. 2020.

I also have notes, from various teaching opportunities that I did not find the time to finish and polish … I put some of them here anyway, partly to motivate myself to take them up again when another opportunity arises.

• Incomplete notes on Introduction to Category Theory. MGS 2017. Chapter 1 contains a long series of beginner’s exercises that should be suitable for self study if you have a mentor who can answer questions.

• An Introduction to Coalgebra and Automata Theory in Three Short Lectures and Two Long (unfinished) Appendices. MGS 2018.