Contents

Idea

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 (…)

Related concepts

• Schur's lemma

• 2-vector space

References

See

• John Baez; Higher-Dimensional Algebra II: 2-Hilbert Spaces (arXiv)

for one approach.