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It's been great teaching this course. While this is the end of the course, there is much more to say about applied category theory, which is quite a large subject. And it's far from done: its best days, I believe, are still ahead. Maybe you can help develop it further!
What should you do next? Well, it makes a lot of sense to finish reading our textbook:
But it will also be good to read this 50-page 'booklet':
Tai-Danae wrote this based on Applied Category Theory 2018; she attended both the 'school' and the following 'workshop'. She's great at explaining things, so this short book is a lot of fun to read.
Tai-Danae focuses on two examples of applied category theory.
First, she explains the 'decorated cospan categories' invented by Brendan Fong when he was doing his thesis with me. These are a general way of dealing with categories where the morphisms are networks. You can learn more about them in Section 6 of Seven Sketches, and even more here:
Brendan used them to study electrical circuits, and we've gone further with that application here:
But Tai-Danae focuses on another application of decorated cospan categories - namely, to chemical reaction networks! This was developed Blake Pollard, another student of mine:
Second, she explains Lambek's approach to linguistics based on 'pregroup grammars'. If you enjoyed how this course focused on posets, I bet you'll really like pregroups. A pregroup is just a monoidal poset that's compact closed!
We started talking about commutative monoidal posets all the way back in Lecture 21, but in applications to linguistics we don't want commutativity - because the order of words matters! We discussed compact closed symmetric monoidal categories in Lecture 74, but Tae-Danae explains more general compact closed categories that are just monoidal, not symmetric monoidal - again, because the order of words matters.
So, if you understood this course, you only need a tiny bit more to get the idea of a pregroup. The fun part is to see how pregroups are used to study words, phrases and sentences!
Lambek was a very interesting guy - perhaps the first to understand the connection between category theory and the lambda calculus - and his work is fun to read:
But the current revival of interest in pregroup grammars may have been started by this paper:
This should be enough to keep you going for a while. I hope you have many pleasant adventures... and don't be afraid to email me at email@example.com with questions or comments!