Every symmetric fusion category over R is equivalent to the semi-linear super representation category of a Z2-graded finite super group.
Finite quantum groupoids and inclusions of finite type
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abstract
Bialgebroids, separable bialgebroids, and weak Hopf algebras are compared from a categorical point of view. Then properties of weak Hopf algebras and their applications to finite index and finite depth inclusions of von Neumann algebras are shortly reviewed. A hint is given at a duality between bialgebroid actions and abstract inclusions in 2-categories.
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Classification of symmetric fusion categories over $\mathbb{R}$
Every symmetric fusion category over R is equivalent to the semi-linear super representation category of a Z2-graded finite super group.