I’m putting together a study group for an introduction to category theory. Who wants to join me?
Usually in the Fall and Winter, I’m concentrating on studying some semblance of abstract mathematics with a group of 20-30 kamikaze amateurs under the apt tutelage of Dr. Michael Miller through UCLA Extension. Since he doesn’t offer any classes in the Spring or Summer and we haven’t managed to talk Terence Tao into offering something interesting à la Leonard Susskind, we’re all at a loss for what to do with some of our time.
A small cohort of regulars from Miller’s class has recently taken up plowing through Howard Georgi’s Lie Algebras and Particle Physics. Though this seems very diverting to me given our work on Lie groups and algebras in the Fall and Winter, I don’t see any direct or exciting applications to anything more immediate.
Why Not Try Category Theory?
Since the death of Grothendieck I have seen a growing number of references to the area of category theory from a variety of different fronts.
Most notably, for the past year I’ve been more closely following John Baez’s Azimuth Blog which has frequent posts relating to category theory with applications I can directly use in various areas. Unfortunately I couldn’t attend his recent workshop at NIMBioS on Information and Entropy in Biological Systems, which apparently means I missed meeting Tom Leinster who recently released the textbook Basic Category Theory (Cambridge University Press, 2014). [I was already never going to forgive myself after I missed the workshop, but this fact now seems to be additional salt in the wound.]
The straw that broke the proverbial camel’s back was my serendipitously stumbling across Ilyas Khan‘s excellent post “Category Theory – the bedrock of mathematics?” while doing a Google image search for something entirely unrelated to anything remotely similar to mathematics. His discussion and the breadth of links to interesting and intriguing papers and articles within it and several colleagues thanking me for posting about it have finally forced my hand. (I also find myself wishing that he would write on a more formal basis more frequently.)
So over the past week or so, I’ve done some basic subject area searching, and I’ve picked up David I. Spivak’s book Category Theory for the Sciences (The MIT Press, 2014) to begin plowing through it.
Anyone Care to Join Me?
Since doing abstract math is always more fun with companions, and I know there are several out there who might be interested in some of the areas which category theory touches on, why don’t you join in? Over the coming months of Summer, let’s plot a course through the subject. I’ll suggest Spivak’s book first as it seems to be one of the most basic as well as the broadest out there in terms of applications. (There are also free copies of versions available through arXiv and MIT.) It doesn’t have a huge list of prerequisites either, so a broader category of people might be able to join in as well.
We can have occasional weekly or bi-weekly “meetings” via internet using something like Google Hangouts, Skype, or ooVoo to discuss problems and help each other out as necessary. Ideally those who join will spend at least 3 hours a week, if not more reading the text and working through problems. Following Spivak, we might try dipping into Leinster, Awody, or Mac Lane.
From the author of Category Theory for the Sciences:
Awody, Steve. Category Theory (Oxford Logic Guides, #52). (Oxford University Press, 2nd Edition, 2010)
Lawvere, F. William & Schanuel, Stephen H. Conceptual Mathematics: A First Introduction to Categories. (Cambridge University Press, 2nd Edition, 2009)
Leinster, Tom. Basic Category Theory (Cambridge Studies in Advanced Mathematics, #143). (Cambridge University Press, 2014)
Mac Lane, Saunders. Categories for the Working Mathematician (Graduate Texts in Mathematics, #5). (Springer, 2nd Edition, 1998)
Spivak, David I. Category Theory for the Sciences. (The MIT Press, 2014)
If you’d like to join us, please leave a comment below and be sure to include your email address in the comment form so we can touch base regarding details.
16 thoughts on “Category Theory Anyone?”
I will be interested.
Although not interested in Driving long distances or in Traffic. Internet would be great.
Also, since there are no major prerequisites and I am am quite busy a “Dummies” version would be most welcome.
Oh man, I really don’t have the time for this but I want to join anyway. I’ve started reading through category theory books (Awodey and MacLane) about 4-5 times in the last couple of years but had to stop. I picked up category theory in grad school but that was ages ago. Anyway I can’t guarantee I will be able to do much more than “audit” but it sounds like fun. Email: email@example.com
Count me in
Depends what night Chris…I’m having a heck of a time carving out space to meet with you guys on Wednesdays. :). I did already start on spivaks book a few months ago in a very cursory overview. Good stuff. Look for another book called Conceptual Mathematics by Schanuel. Seems like a lot of overlap between the two but it has some good Intro level insights as well so might not be a bad supplement.
I’m a possibility, thanks. Depends on my location but would love to be kept apprised.
I’m interested. firstname.lastname@example.org
This Article was mentioned on boffosocko.com
if its not too late I would love to join (email@example.com)
Chris Aldrich is organizing an online category theory study group for summer 2015; preliminary syllabus here
#category theory, #mathema, #chris aldrich
eka-mark mentioned this Article on eka-mark.tumblr.com
I’m interested (zcarterc gmail com).
For those who aren’t aware yet, I’ve posted a tentative syllabus with schedule and some administrative questions. If you haven’t already, take a moment to read the post and fill out the details at the bottom.
Chris Aldrich mentioned this article on stream.boffosocko.com.
Reading list on category theory, from study group friend attended organised by Chris Aldrich (JHU biomed/elec eng.) boffosocko.com/2015/05/21/cat…