Lecture 1 - Introduction
Hi, I'm John Baez. Welcome to the lectures from my Applied Category Theory Course!
Back in 2018 I decided to teach an online course because I was getting bored of the superficial engagement I'd been getting on my social media posts, mainly on Google+, which started out great but then went downhill (and later died). I like to explain things, discuss things and learn things by talking to people. I've been doing this for decades, first on sci.physics.research, and later on the n-Category Café, the Azimuth blog... and the Azimuth Forum here, which began life as a platform for creating a wiki about environmental issues: the Azimuth Wiki. All these fora were great fun, but it seems each one got a bit stale after a while, so I felt it was time for something new.
I decided to teach a course on applied category theory because that's what I was working on, and my former student Brendan Fong was doing a postdoc with David Spivak at MIT, and they taught a course on this subject and turned it into a very nice book that you can download for free:
- Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.
My course was based on this book. I gave "lectures" on it - in print, like this one here - from March 2018 until September 25th, when I had to start teaching classes at U. C. Riverside again. The book has 7 chapters, but I only managed to cover the first 4.
I tried to write a short lecture every day or so, sometimes more than one. But sometimes I was busy: most notably, from April 23rd to May 5th, Brendan, David and I went to the Netherlands for Applied Category Theory 2018, along with 60 other people, and things will get very hectic. I also slowed down near the end.
Students did almost all the exercises in the book, and I also posed a lot of puzzles, but at this point it would be quite a job to copy the answers over to this website.
So, for now, here are the lectures. If you have questions, please join the Category Theory Community Server - an online discussion group that I frequent - and ask your questions there! They will almost surely get answered either by me or someone else.
With luck, you will learn a lot of stuff, make a lot of new friends... and go ahead to revolutionize human thought, invent amazing new technologies, and save the planet.
The book Seven Sketches has a bibliography with some good reference. Wikipedia is actually very good for definitions of terms used in category theory. For more advanced material, see the nLab. Also try these free books:
Tom Leinster, Basic Category Theory, Cambridge Studies in Advanced Mathematics, Vol. 143, Cambridge University Press, 2014. (An introduction.)
Emily Riehl, Category Theory in Context, Dover, New York, 2016. (More advanced.)
To read other lectures go here.