Some of us in the PL/Vis lab are starting a reading group to study Category Theory (that was co-founded right here in Chicago by Saunders Mac Lane) over the summer. We will be working through the book Category Theory for Computing Science by Michael Barr and Charles Wells.
Aim to read and do many (if not most) of the exercises in chapters 2 through 6.
Meet once or twice a week to
discuss a section of the text (examine and explain the harder material) and
present solutions to a selection of exercises in the text. 2 is more important than 1.
Compile these solutions into a PDF of some sort.
We are currently planning to meet for the first time on 2019-07-09T17:00:00Z at JCL 280 (bring your own lunch). We expect to come prepared to discuss Ch-2.
If you are interested, you should join @CTRG group, so we can keep you in the loop. See you next week!
Finally, if you are not physically on campus during the summer, worry not, we plan to include a Skype (or some other teleconferencing system) call as well as I will be away too for part of the summer. Details TBD.
Four of us met this afternoon, 3 in person and I remotely over Skype (thanks to @andreweckart). We were glad that Prof. Gerry Brady could make it this time.
We mostly discussed some previous exercises. Here’s the plan for next week:
Work through exercises from sections 2.5 to 2.9, skip those that seem too easy.
Understand concepts and proofs in 2.10 as they seem non-trivial. Attempt exercises.
I would like to suggest Peter Smith’s book Gentle as an additional reference. The topic order is weird but I found it very useful during my undergrad to lookup certain concepts which I couldn’t properly understand. The explanations imo are very good (and gentle!).
Just to recap our meeting from last Wednesday, Sept 4:
We spent most of the meeting discussing the definition of the Yoneda embedding and proof of the eponymous lemma in CTCS.
The assigned work was to examine the proofs independently and write them out by hand. Our next topic is adjunction, as discussed in Ch. 2 of Tom Leinster’s Basic Category Theory.
Hey @teocollin, @andreweckart, do you recall what we decided for our last meeting coming up this Wed? Sorry, I seem to have completely forgotten.
Are we doing Ch-5 (Products and sums), 6 (Cartesian Closed Categories) in Barr and Wells or those two in Leinster (ie, Limits and the concluding chapter)?
So instead of meeting as usual last Wed, we decided to just chat over lunch.
I want to share some concluding thoughts as the summer and the reading group comes to an end and some resources for others interested in learning Category Theory that we found useful:
Bartosz Milewski’s Category Theory for Programmers is the most accessible introduction for people with little math background, but some exposure to programming languages such as Haskell and C++.
The main textbook we used for this reading group, Barr and Wells (there is also a shorter version of this book), is good for basics, but we found the exercises to be lacking. I also personally disliked how many backreferences the book has for both exercises and reviews of previous concepts that lead to one needing to constantly go back and forth without any hyperlinks in the book’s PDF (EDIT: there is now a hyperlinked version available.
Leinster’s book is quite good for building intuition, but one may want to ignore the examples that are from unfamiliar sub-fields of Mathematics as the author himself suggests in the Preface. The exercises are more interesting than the previous book.
When I look at papers related to the semantics of quantum programming languages now, I seem to have a much better understanding of their presentation and contribution. This alone is a great outcome for me of having attended this reading group. Thanks to everyone who attended and kept the group going. Special thanks to @teocollin and @tushant for being our teachers and motivators and @andreweckart for his enthusiasm. Thanks also to @gb52 for her support and attendance.
Please feel free to share any thoughts or questions. I, for one, want to continue learning more of Category Theory as and when I get more opportunities outside of my own research.
If you are looking to see the current research frontier in Category Theory during the COVID-19 crisis, there are several online seminars happening now:
Should have replied to this sooner… I am still in the planning stages, but it will likely be at the end of July or beginning of August, and will be primarily focused on categorical semantics and the various categorical type theory correspondence theorems (algebraic theories and categories with finite products, stlc and cartesian closed categories, dtlc and locally cartesian closed categories, etc.) Keep an eye out for details, hopefully soon.