Lecture 1 - Introduction

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:

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:

To read other lectures go here.

© 2018 John Baez