Description
It is commonly expected that n-dimensional topological quantum field theories and their interfaces assemble into an n-category.
In this talk, I will suggest a list of reasonable assumptions satisfied by such an n-category of (discrete and semisimple) TQFTs, including Freed and Hopkins’ suggestion that invertible theories are completely determined by their partition functions on closed manifolds. I will then explain that there is a unique n-category satisfying these assumptions, and — if time permits — sketch how it looks in low dimensions.
This is based on work in progress with Theo Johnson-Freyd.