The concept of $2$-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.

Last revised on September 24, 2018 at 14:46:33. See the history of this page for a list of all contributions to it.