String-net models for pivotal bicategories
J Fuchs, C Schweigert, Y Yang - arXiv preprint arXiv:2302.01468, 2023 - arxiv.org
We develop a string-net construction of a modular functor whose algebraic input is a pivotal
bicategory; this extends the standard construction based on a spherical fusion category. An …
bicategory; this extends the standard construction based on a spherical fusion category. An …
Grothendieck-Verdier duality in categories of bimodules and weak module functors
J Fuchs, G Schaumann, C Schweigert… - arXiv preprint arXiv …, 2023 - arxiv.org
Various monoidal categories, including suitable representation categories of vertex operator
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …
algebras, admit natural Grothendieck-Verdier duality structures. We recall that such a …
The distinguished invertible object as ribbon dualizing object in the Drinfeld center
We prove that the Drinfeld center $ Z (\mathcal {C}) $ of a pivotal finite tensor category
$\mathcal {C} $ comes with the structure of a ribbon Grothendieck-Verdier category in the …
$\mathcal {C} $ comes with the structure of a ribbon Grothendieck-Verdier category in the …
Categorical generalisations of quantum double models
AK Hirmer, C Meusburger - arXiv preprint arXiv:2306.05950, 2023 - arxiv.org
We show that every involutive Hopf monoid in a complete and finitely cocomplete symmetric
monoidal category gives rise to invariants of oriented surfaces defined in terms of ribbon …
monoidal category gives rise to invariants of oriented surfaces defined in terms of ribbon …