Hopf algebras and 3-categories

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• David Reutter (Oxford)
• Friday 27 April 2018, 15:00-16:00
• MR13.

If you have a question about this talk, please contact Nils Prigge.

It is well known that commutative Frobenius algebras can be represented as oriented surfaces, using the graphical calculus of dualizable objects in monoidal 2-categories. I will build on related ideas to show that certain Hopf algebras arise naturally in a similar way, by requiring a single 3-morphism in a 3-category to be invertible. This gives a purely geometrical proof of Mueger’s version of Tannakian reconstruction of Hopf algebras from fusion categories equipped with a fiber functor. This talk is intended as an informal introduction to several topological ideas in categorical algebra, I will not assume any previous knowledge of the subject.

This talk is part of the Junior Geometry Seminar series.

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