Lecture 1 - Introduction
Welcome to the Applied Category Theory Course! You can register at left using your full real name as username.
I haven't carefully counted, but so far about 150 of you have registered, and I see 27 more applicants whom I haven't gotten around to approving. A bunch of you have written self-introductions; I haven't gotten around to responding to all these yet either - but it's obvious we've got a formidable team here. If we work together we can do amazing things.
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 has been going downhill. 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 gets a bit stale after a while, so it's time for something new.
I decided to teach a course on "applied category theory" because that's what I'm working on, and my former student Brendan Fong is 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.
Our course will be based on this book. I'll give "lectures" on it - in print, like this one here - from now until at most September 25th, when I have to start teaching classes at U. C. Riverside again. The book has 7 chapters, and we've got at most 6 months. I don't have a set time-table: we'll have to see how things go. We could be done much sooner, but it may be fun to go slower and get into more detail.
I will try to write a short lecture every day or so, sometimes more than one. But sometimes I'll be busy: most notably, from April 23rd to May 5th, Brendan, David and I will be in the Netherlands at Applied Category Theory 2018, along with 60 other people, and things will get very hectic. Expect a slowdown or complete silence then. With luck you can watch videos.
We should do all the exercises in the book. I hope some of you volunteer to copy these exercises over to the Forum, one at a time, so we can talk about them here. I'll get the game started but I can't do everything.
I will also pose Puzzles. In fact I've already started!
So, your job is to read the book, ask questions, try to do the Exercises and Puzzles, write your answers here - and most importantly, discuss everything to death! There will be a place to discuss each Chapter, and a place to discuss each Lecture and these discussions can go on indefinitely.
I will take part in these discussions - that's what I love about online forums. But if all of you ask lots of questions - and I really hope you do! - I'll be unable to answer them all myself. So, it's crucial that if someone asks a question, and you think you know the answer, help them out.
With luck, we'll all learn a lot of stuff, make a lot of new friends... and some of us will go ahead to revolutionize human thought, invent amazing new technologies, and save the planet.
Getting to Know Each Other
If you're new to the Azimuth Forum, please post a comment about your interests and background in the category Chat. A lot of you have already done this. So, go read some - and reply to at least one! Pick one that hasn't gotten any replies yet. I want to go through them all and reply to every one, but it will take me a while. If you get to know some other people in the course, it'll be a lot more fun.
I'd like to keep the discussions on Chapters (of the book) and Lectures (like this) fairly focused. There is always conversation drift, and some of that is okay, but if you start wanting to talk about algebraic geometry or sky-diving or something else that's not really about the course, please take it to Chat. That's a good place for free-wheeling discussions.
Discussions
You discuss the Chapters by posting a comment on the appropriate thread, like this:
You can discuss my Lectures by posting a comment on its thread. If you have questions or comments on the subject of the course that don't quite fit into any of these places, you can start a new discussion in the category Applied Category Theory Course. If you have questions about technical aspects of how the Azimuth Forum works - or why it's not working - start a discussion in the category Technical.
Writing math
You can write equations using
MathJax, which is a
limited version of LaTeX good for the web. For "displayed" equations,
centered on the page, use double dollar signs: {% math %}E = \sqrt{m^2 +
p^2}{% endmath %} produces this:
For "inline" equations, mixed in with your text, use this other
method: \\(E = \sqrt{m^2 + p^2}\\) produces this: \(E = \sqrt{m^2 +
p^2}\). If you don't know anything about LaTeX, you can look at the
source code of other people's comments and see how they're doing
stuff.
Resources
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.)
Be nice
It's an inevitable feature of any discussion forum that some users become rude, bully others, try to take over conversations, or try to promote irrelevant ideas. Anyone who becomes annoying in these or other ways will be banned. I won't allow discussions about these issues, either. I have been helping run online discussion forums since around 1989, back when we used modems, and I've learned that requiring politeness is the only way to keep attention focused on the actual subject matter. If you don't want to be polite and respectful of others, please leave now.
Pro tip: if someone says something idiotic, like "all categories have colimits", don't say "You're wrong." Say "Actually not all categories have colimits: consider for example the category of free groups and homomorphisms between those." It's amazing how much better people respond when they don't perceive a correction as being an attack on their person. People are incredibly sensitive things.
Click here to read the original discussion
License
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