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)
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!)