A universal property of the higher category of spans and finite gauge theory as an extended TFT

Online talk.

I will explain how to generalize Harpaz’ universal property of the (infty, 1)-category of spans to the higher category thereof. The crucial property is “m-semiadditivity”. Combining this with the finite path integral construction of Freed-Hopkins-Lurie-Teleman this yields finite gauge theory as a fully extended TFT. This is joint work in progress with Tashi Walde.