**Theorem 1.** This course is awesome.

*Proof:* John, thanks very much for your idea of teaching this course to all of us. Having your Lectures to supplement the book has been tremendously useful; I don't think I would have understood the material if I had just read the book on my own.

I'm still finishing my digestion of Chapter 3. I haven't posted much, but I'm definitely still here! It's been surprisingly difficult to establish an intuition for adjunctions, but I'm glad you've given us enough detail to make the effort, because I can tell it's important material and struggling through it makes me feel like I'm really learning something and not just being a tourist.

I look forward to starting on Chapter 4 and reading all the stuff you've written for us. If you decide to make this a 4-month (free!) course instead of a 6-month course, I'm sure we'll all understand and still appreciate your efforts just as much.

I wonder if it would be helpful and fun if you ended with a few "greatest hits" lectures to give us a taste of the later material without trying to teach it thoroughly. If you gave us some idea of what we're missing, and why it's exciting, that might help us stick with the subject and continue our self studies. I'd like to know other things, like adjunctions and monoidal categories for example, that you consider especially important if one wants to get a true sense of how category theory is put together.

One bit of feedback if you decide to do another course next summer. I appreciate the give and take in the comments as you let us students work through the puzzles ourselves. However, all the confusions and false starts make the comment thread less useful as a reference when I go back to a lecture for repeat study. When you give us puzzles to solidify our understanding, it would be helpful if the discussion could be distilled to a correct set of answers "blessed" by you. Perhaps after a couple of weeks you could pick correct student answers and copy them into an answers thread or some sort of hidden spoiler tag? That would make the Lectures a more useful long-term reference, if it's not too much work.

The forum software makes it hard to sustain conversations in old threads, especially without a working notification system, or a place for "front page" announcements. It can feel lonely once someone has fallen behind. I wonder if something like periodic email surveys could reveal whether there's a substantial number of students still working through earlier sections. If so, perhaps it would be good to have a "rest week" now and then for everyone to go back and try some new puzzles together to help those students catch up. But I guess realistically, once someone falls way behind they're more likely to stop attending the course altogether.

Perhaps you could reduce the effort somewhat by spacing out the Lectures more? For example, what if you followed each Lecture with a day or two where all you do is add new puzzles for that topic. This might also give students less speedy with the material more chances to get first crack at a puzzle, rather than the "usual suspects".

Thanks again for the course! It has been awesome. \\( \blacksquare \\)