Idk, as a mathematician, I still don’t really see the usefulness of category theory “in the real world” (or even in a good amount of math)
Differential Equations Statistics / Stochastic Processes Discrete Math / Algorithms / Logic Solver
You do not need CT for all this stuff.
Grothendieck needed CT - ist Algebraic Geometry useful?
I've read the paper. They list many useful applications. CT doesn't seem really necessary for each of them but it looks like CT is (could be) helpful.
It is just very hard to create non-trivial general theories in sich „Applied“ fields, Functional Analysis alone is not very exciting. For an example see for example the work or Hairer (stochastic differential equations) or Costello (QFT).
This is wild stuff:
https://people.math.umass.edu/~mirkovic/0.SEMINARS/1.QFT/C.C...
funny names: a Leonard Cohen writing about an Costello (but Kevin Costello not Elvis Costello)