What I mean by higher level before this gets closed is functional analysis, complex analysis and harmonic analysis?
I've read looked at the examples in most category theory books and it normally has little Analysis. Which, is strange as I've even seen lattice theory be used to motivate a whole book on category theory.
I was wondering is there a nice application of category theory to functional analysis?
It's weird as read that higher category theory is used in Quantum mechanics as it foundation, yet QM has heavy use of Hilbert spaces.