Reduced Tensor Product on the Drinfeld Center

Abstract

The annulus comes with a "stacking" operation which glues two annuli into one. This provides a tensor product structure on the category of boundary values $Z_{\text{CY}}(\text{Ann})$ associated to the annulus in an extended Crane-Yetter TQFT. It is known that $Z_{\text{CY}}(\text{Ann})\simeq \mathcal{Z}(\mathcal{A})$, the Drinfeld center of the premodular category $\mathcal{A}$ from which $Z_{\text{CY}}$ is constructed. We give an explicit formula for the tensor product on $\mathcal{Z}(\mathcal{A})$ that corresponds to the stacking operation on $Z_{\text{CY}}(\text{Ann})$.

update: revision for resubmission

References in corpus (3)

• String-net model of Turaev-Viro invariants
• Excision of Skein Categories and Factorisation Homology
• Factorization Homology and 4D TQFT

Cited by in corpus (3)

• Minimal nondegenerate extensions
• On the Category of Boundary Values in the Extended Crane-Yetter TQFT
• Categorical Center of Higher Genera and 4D Factorization Homology