[MSE-SOLVED] Subfunction is functorial!!!!

[JmsNxn]

...
So the next question we should ask is: does the subfunction functor have adjoints??

I can't remember off the top of my head; but there's a relation between adjoints in category theory and adjoints in functional analysis, and the dual space. That would be super cool. My dream was always a functional space where you can do hyper operators...

I think it might be beneficial for me to dust off my hilbert space textbooks. I think looking at,

\(
\uparrow f= \frac{d^{z-1}}{dw^{z-1}}|_{w=0} \sum_{n=0}^\infty f^{\circ n+1}(a)\frac{w^n}{n!}\\
\)

with an inner product may be important. Of course we'll have to be in a restricted kind of space; and only consider bounded super-functions with an attracting fixed point of real-positive multiplier.