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 $Z_{ \text{ CY}}(\text{ Ann})$.
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