homotopy hypothesis-theorem delooping hypothesis-theorem stabilization hypothesis-theorem A concept of -Hilbert spaces is supposed to be a categorification of that of Hilbert spaces, or at least of finite dimensional such: inner product spaces. One way to define this is as a Kapranov-Voevodsky 2-vector space where the hom-functor plays the role of the categorified inner product (Baez 96). In other words, a -Hilbert space is an abelian -category. More generally this works for semisimple...