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We study unitary pseudonatural transformations (UPTs) between fibre functors Rep(G) -> Hilb, where G is a compact quantum group. For fibre functors F_1, F_2 we show that the category of UPTs F_1 -> F_2 and modifications is isomorphic to the category of finite-dimensional *-representations of the corresponding bi-Hopf-Galois object. We give a constructive classification of fibre functors accessible by a UPT from the canonical fibre functor, as well as UPTs themselves, in terms of Frobenius algebras in the category Rep(A_G), where A_G is the Hopf *-algebra dual to the compact quantum group. As an example, we show that finite-dimensional quantum isomorphisms from a quantum graph X are UPTs between fibre functors on Rep(G_X), where G_X is the quantum automorphism group of X.
We give an elementary and direct combinatorial definition of opetopes in terms of trees, well-suited for graphical manipulation and explicit computation. To relate our definition to the classical definition, we recast the Baez-Dolan slice constructio
A unitary fusion category is called $mathbb{Z}/2mathbb{Z}$-quadratic if it has a $mathbb{Z}/2mathbb{Z}$ group of invertible objects and one other orbit of simple objects under the action of this group. We give a complete classification of $mathbb{Z}/
We compute the group of braided tensor autoequivalences and the Brauer-Picard group of the representation category of the small quantum group $mathfrak{u}_q(mathfrak{g})$, where $q$ is a root of unity.
This article investigates duals for bimodule categories over finite tensor categories. We show that finite bimodule categories form a tricategory and discuss the dualities in this tricategory using inner homs. We consider inner-product bimodule categ
We develop the rewriting theory for monoidal supercategories and 2-supercategories. This extends the theory of higher-dimensional rewriting established for (linear) 2-categories to the super setting, providing a suite of tools for constructing bases