nLab
Moore-Seiberg data

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

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

where $1$ is the unit object of $𝒞$.

References

Bojko Bakalov and Alexander Kirillov, Lectures on Tensor Categories and Modular Functors, University Lecture Series 21, AMS.

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