nLab H-star-category

Idea

A $H^*$-category is a categorification of the notion of an $H^\ast$-algebra.

Definition

Definition

An $H^*$-category is a $\mathrm{Hilb}$-category with a $\dagger$-structure that defines an antinatural transformation? from $\operatorname{hom}(x,y)$ to $\overline{\operatorname{hom}(y,x)}$, where $\overline{\operatorname{hom}(y,x)}$ is the conjugate hom-Hilbert space.

(Baez 1996 Def. 2)

Related concepts

• H-star-algebra

• 2-Hilbert space

References

Introduced in:

• John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997) 125-189 [arXiv:q-alg/9609018]