# Frobenius algebras, Hopf algebras and 3-categories

### APA

Reutter, D. (2017). Frobenius algebras, Hopf algebras and 3-categories. Perimeter Institute. https://pirsa.org/17080011

### MLA

Reutter, David. Frobenius algebras, Hopf algebras and 3-categories. Perimeter Institute, Aug. 03, 2017, https://pirsa.org/17080011

### BibTex

@misc{ pirsa_PIRSA:17080011, doi = {10.48660/17080011}, url = {https://pirsa.org/17080011}, author = {Reutter, David}, keywords = {Quantum Foundations, Quantum Information}, language = {en}, title = {Frobenius algebras, Hopf algebras and 3-categories}, publisher = {Perimeter Institute}, year = {2017}, month = {aug}, note = {PIRSA:17080011 see, \url{https://pirsa.org}} }

Universität Hamburg

Talk Type

Abstract

It is well known that commutative Frobenius algebras can be represented as topological surfaces, using the graphical calculus of dualizable objects in monoidal 2-categories. We build on related ideas to show that the interacting Frobenius algebras of Duncan and Dunne, which have a Hopf algebra structure, arise naturally in a similar way, by requiring a single 3-morphism in a 3-category to be invertible. We show that this gives a purely geometrical proof of Mueger's version of Tannakian reconstruction of Hopf algebras from fusion categories equipped with a fibre functor. We also relate our results to the theory of lattice code surgery.