nLab Moore-Seiberg data

Idea

Moore–Seiberg data are structure constants for a modular tensor category, seen as a Frobenius algebra in the 2-category of $Vect_k$-enriched abelian categories. More explicitely, Moore–Seiberg data for the modular tensor category $\mathcal{C}$ are the collections of $k$-vector spaces

$$\langle X_1,\dots,X_n\rangle=Hom_\mathcal{C}(\mathbf{1},X_1\otimes\cdots\otimes X_n),$$

where $\mathbf{1}$ is the unit object of $\mathcal{C}$.

References

• Bojko Bakalov, Alexandre Kirillov: Lectures on tensor categories and modular functors, University Lecture Series 21, Amer. Math. Soc. (2001) [webpage, ams:ulect/21, pdf]

• Gregory Moore and Nathan Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123 (1989), 177–254.