I’ve been reading the “relevance for supersymmetry” of the nlab article on Deligne’s theorem, and had a few niggling doubts: doesn’t this only apply to finite-dimensional vector spaces?

More specifically: Hilbert spaces don’t categorify well, and I’m not aware of any ‘reasonable’ category built on them which abelian. Thus, I can’t see any natural way in which representations on them form a tensor category.

Since everything works out nicely in finite dimensions, what I *can* see is that Deligne’s theorem implies that the most general symmetries of a finite-dimensional quantum system are given by algebraic super-groups. (Well, almost – one also has to admit antilinear representations by Wigner/Bargmann, so even this doesn’t seem exactly true.)

So here is my question: am I missing something?

]]>Foundations of Systems Architecture Design

Using Gödel’s Incompleteness Theorem to ground Systems Theory via Co-recursion based on Special Systems Theory

See https://www.academia.edu/31038671/Foundations_of_Systems_Architecture_Design

I was hoping someone here might be able to help me who would find this approach interesting.

Kent Palmer

http://kdp.me

https://independent.academia.edu/KentPalmer ]]>