nLab fusion 2-category


2-category theory

Monoidal categories

monoidal categories

With braiding

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products



Internal monoids



In higher category theory



A categorification of the notion of fusion categories to 2-categories.


Tannaka-Krein reconstruction theorem

The Tannaka duality establishes a correspondence between (multi-)fusion categories and weak Hopf algebras. It is expected that an analogous statement holds for the higher categorification of this setting. The theorem corresponding to the specialization of this setting to fusion 2-categories and semisimple Hopf categories (as opposed to multi- fusion 2-categories and weak Hopf categories) appears in (Green (2023)).


(Tannaka-Krein reconstruction theorem for fusion 2-categories)

There is a symmetric monoidal equivalence, contravariant at the level of 1-morphisms, between the full subcategory of 3Vec/2Vec3Vec/2Vec consisting of locally faithful functors and the 2-category of 2-Hopf Algebras. The natural transformations associated to this equivalence reconstruct a semisimple Hopf category from its fusion 2-category of representations and fiber functor, and a fusion 2-category with fiber functor FF from the Hopf category End(F)End(F).


Last revised on September 16, 2023 at 18:37:34. See the history of this page for a list of all contributions to it.