It may be professional deformation speaking, but they seem to be using "applied category theory" in a coherent and natural sense: they mean the theory of monoidal categories, (a) viewed as a generalization of linear algebra, and (b) omitting logic and programming language semantics as applications.

Given the centrality of linear algebra to applied mathematics (even in places where you wouldn't first expect, like the theory of regular expressions and finite automata), this seems like a perfectly sensible coinage.

(Even though I must admit I get my back up at the omission of categorical proof theory, it's perfectly natural as a sales pitch -- type theorists don't need to be convinced of the utility of category theory!)

> Given the centrality of linear algebra to applied mathematics (even in places where you wouldn't first expect, like the theory of regular expressions and finite automata)

Where can I read more about this?

Stephen Dolan's pearl "Fun with semirings" might be relevant:

http://stedolan.net/research/semirings.pdf

But I would also like to know what other resources Neel has to recommend.

If you like Matlab more than Haskell, try https://www.goodreads.com/book/show/11768822-graph-algorithm...

"Applied Category Theory" almost seems a bit tongue-in-cheek to me, given Category Theory is designed to distill the concepts found in a bunch of different "applied" fields into one, theoretical, framework. (That was my impression from the intro lecture, at least)

They should call the class “Concrete Nonsense” (since category theory itself is sometimes described as “abstract nonsense”).

Which phrase, I note with profound glee, has its own Wikipedia page for precisely this usage:

https://en.wikipedia.org/wiki/Abstract_nonsense

Maybe “Brutalist Nonsense”