The Drinfeld center of a monoidal category, which is a braided monoidal category.
The Drinfeld center of a monoidal category $\mathcal{C}$ is the braided monoidal category $\mathcal{Z}(\mathcal{C})$ given by:
- Objects: Tuples $(X, \gamma)$, where $X$ is an object of $\mathcal{C}$, and the half-braiding $\gamma_Y\colon Y \otimes X \to X \otimes Y$ is a natural isomorphism satisfying a hexagon axiom.
- Morphisms: Morphisms from $\mathcal{C}$ that are compatible with the half-braiding.
Notably, the Drinfeld center is a braided category, with the braiding given by the half-braiding. If $\mathcal{C}$ is a spherical fusion category, its Drinfeld center is modular.
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