Corpus ID: 119269075

# Unitary dual functors for unitary multitensor categories

@article{Penneys2018UnitaryDF,
title={Unitary dual functors for unitary multitensor categories},
author={David Penneys},
journal={arXiv: Quantum Algebra},
year={2018}
}
• David Penneys
• Published 2018
• Mathematics
• arXiv: Quantum Algebra
• We classify which dual functors on a unitary multitensor category are compatible with the dagger structure in terms of groupoid homomorphisms from the universal grading groupoid to $\mathbb{R}_{>0}$ where the latter is considered as a groupoid with one object. We then prove that all unitary dual functors induce unitarily equivalent bi-involutive structures. As an application, we provide the unitary version of the folklore correspondence between shaded planar ${\rm C^*}$ algebras with finite… CONTINUE READING

#### Citations

##### Publications citing this paper.
SHOWING 1-8 OF 8 CITATIONS

## Representations of fusion categories and their commutants.

• Mathematics
• 2020

## Realizations of Rigid C*-Tensor Categories as Bimodules over GJS C*-Algebras

• Mathematics
• 2020

## The module embedding theorem via towers of algebras.

• Mathematics
• 2018

## Free oriented extensions of subfactor planar algebras

• Mathematics
• 2018

## Deligne categories in lattice models and quantum field theory, or making sense of O(N) symmetry with non-integer N

• Physics, Mathematics
• 2020
VIEW 1 EXCERPT

## The Extended Haagerup fusion categories

• Mathematics
• 2018
VIEW 9 EXCERPTS
CITES METHODS & BACKGROUND

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 41 REFERENCES

## Realizations of algebra objects and discrete subfactors

• Mathematics
• 2017

## Planar algebras in braided tensor categories

• Mathematics
• 2016

## Dualizable tensor categories

• Mathematics
• 2013
VIEW 2 EXCERPTS

## Minimal Index and Dimension for 2-C*-Categories with Finite-Dimensional Centers

• Mathematics, Physics
• 2018

## Categorified trace for module tensor categories over braided tensor categories

• Mathematics
• 2015

## Constructing the extended Haagerup planar algebra

• Mathematics
• 2012

## The module embedding theorem via towers of algebras.

• Mathematics
• 2018

## Fixing the functoriality of Khovanov homology

• Mathematics
• 2009

## Dualizability and index of subfactors

• Mathematics, Physics
• 2011