Related papers: Q-systems and compact W*-algebra objects

A Q-system in a C* 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C* 2-categories called Q-system…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

A Q-system is a unitary version of a separable Frobenius algebra object in a C*-tensor category or a C*-2-category. We prove that, for C*-2-categories $\mcal C$ and $\mcal D$, the C*-2-category $\textbf{Fun}(\mcal C, \mcal D)$ of $ * $-$ 2…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

We consider certain categorical structures that are implicit in subfactor theory. Making the connection between subfactor theory (at finite index) and category theory explicit sheds light on both subjects. Furthermore, it allows various…

This paper studies Frobenius subalgebra posets in abelian monoidal categories and shows that, under general conditions--satisfied in all semisimple tensor categories over the complex field--they collapse to lattices through a rigidity…

A certain class of Frobenius algebras has been used to characterize orthonormal bases and observables on finite-dimensional Hilbert spaces. The presence of units in these algebras means that they can only be realized finite-dimensionally.…

A Q-system is a unitary version of a separable Frobenius algebra object in a C*-tensor category. In a recent joint work with P. Das, S. Ghosh and C. Jones, the author has categorified Bratteli diagrams and unitary connections by building a…

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

Q-systems are unitary versions of Frobenius algebra objects which appeared in the theory of subfactors. In recent joint work with R. Hern\'andez Palomares and C. Jones, the authors defined a notion of Q-system completion for C*/W*…

We prove the equivalence of two tensor products over a category of W*-algebras with normal (not necessarily unital) *-homomorphisms, defined by Guichardet and Dauns, respectively. This structure differs from the standard tensor product…

Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on…

We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting actions of two compact quantum groups…

We show that the bigroupoid of separable symmetric Frobenius algebras over an algebraically closed field and the bigroupoid of finitely semi-simple Calabi-Yau categories are equivalent. To this end, we construct a trace on the category of…

We use the theory of regular objects in tensor categories to clarify the passage between braided multiplicative unitaries and multiplicative unitaries with projection. The braided multiplicative unitary and its semidirect product…

Let $G$ be a group. We give a categorical definition of the $G$-equivariant $\alpha$-induction associated with a given $G$-equivariant Frobenius algebra in a $G$-braided multitensor category, which generalizes the $\alpha$-induction for…

This paper addresses the problem of describing the structure of tensor C*-categories M with conjugates and irreducible tensor unit. No assumption on the existence of a braided symmetry or on amenability is made. Our assumptions are…

The tensor functor called $\alpha$-induction produces a new unitary fusion category from a Frobenius algebra, or a $Q$-system, in a braided unitary fusion category. A bi-unitary connection, which is a finite family of complex number subject…

We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an application we give a new construction of the functor that assigns…

In the first part of this article we prove that one of the conditions required in the original definition of nearly Frobenius algebra, the coassociativity, is redundant. Also, we determine the Frobenius dimension of the product and tensor…