[CTRG] Category Theory Reading Group

So we had 4 people attend the first meeting earlier this afternoon. @teocollin graciously led the discussion.

We only covered up to the end of section \S2.4 with a major chunk of time near the end spent on understanding Example 2.4.9

Next steps

  • Exercise assignments:
    \S1: Andrew (has already done half of them)
    \S2: @andreweckart
    \S3: @kartik
    \S4: Kartik and Andrew will divide and conquer
  • Continue with the rest of the chapter
  • We are planning to move the meeting to Wed lunch slot
  • Kartik to participate remotely (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.
  • Read Ch-3.
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The same four of us met again today (me over Skype).

More exercise discussion on sections 2.7 and 2.8. Next week:

  • Work through rest of the exercises in Chapter 2 (2.9 and 2.10).
  • Finish Ch-3
  • @teocollin to investigate over the weekend what other chapters to read and in what order. We may also consider supplementing with other resources.

PS: I will attend physically from next week on. :slight_smile:

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Looks like the reading group is stable now as the same 4 of us met this week as well.

We discussed some exercises from 2.9 and some from Ch-3 and mostly did planning for the rest of the time.

Here’s the new plan for rest of the time:

  • Finish Ch-3 on Functors with selected exercises
  • Finish Ch-4 Diagrams, naturality and sketches
  • Move on to Tom Leinster’s Basic Category Theory which is available free online.
    • Do Ch-2 Adjoints
    • Look at The Yoneda Lemma in Ch-4
  • Return to Barr and Wells and continue with Ch-5 and 6

Plan for next week:

  • @andreweckart and @kartik to meet over the weekend to work on exercises in Ch-3.
  • The goal is to finish Ch-3, but reading ahead is always okay.

We met after two weeks today. @tushant joined us this time.

Discussed exercises from sections 3.1, 2.10.

Next week: Finish Ch-3, specifically 3.4 Equivalences and 3.5 Quotient Categories.

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!).

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Last week four of us met and discusses concepts and exercises from the remaining sections of section 3.

This week, we aim to finish up to section 4.4 in Barr and Wells.

We met today and discussed some exercises from 4.2.

Next week:

  • Finish Ch-4 (Yoneda Lemma and Sketches)
  • Write one exercise from each section

Aside, apparently primary school kids can be taught category theory (I don’t think I know much about knots, however):

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.

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Sorry but I will not be able to make it today.

Gerry

Three of us met today and studied adjunctions mostly with the help of exercises based on vector spaces from Leinster’s book.

Next week:

  • We will be meeting at 1-2pm instead of the usual time (an hour later) as I have to be at a talk at lunch.
  • Ch-4 in Leinster.

There are just two more meetings left before Autumn quarter starts, so feel free to pick other topics that you may want to discuss and share here.

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.
  • Peter Smith’s collection of resources can be used for other tastes. His own book is a handy reference for most concepts.

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:

do you plan on running this again this coming school year?

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I am not, but I have heard that @nmull is planning a reading group on Categorical Logic this summer. I will let him share the details.

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.

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Just letting everyone know that I’m postponing the categorical logic reading group a bit (not surprising given how long its been since I said anything about it…). Still hoping to get going some time August.

For those keeping an eye on this (which I assume is few to none) I don’t have the energy right now to do the reading group during the summer. I’m going to save it for the fall, or for when we can meet in person.

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