The concept of -Hilbert space is supposed to be a categorification of that of Hilbert space, 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).
More generally this works for semisimple categories (…)
See
for one approach, and
for a refinement of this approach.
A treatment of 3-Hilbert spaces, the further categorification of 2-Hilbert spaces, is in
Last revised on October 21, 2024 at 08:23:56. See the history of this page for a list of all contributions to it.