4d TFTs, Categorical bialgebras, and 2-Segal spaces

In the 90s Crane-Frenkel proprosed the construction of a 4d TQFT from a bimonoidal category, that is, a category equipped with both a monoidal and comonoidal structure so that the data defining the comonoidal structure is itself monoidal. In this talk I will explain a conceptual reason for the connection between bialgebras and TFTs. Secondly, I will describe how to extend the classical construction of the Hall algebra of an abelian category to produce new examples of bimonoidal categories: the Hall bimonoidal categories. The approach taken is based on the theory of 2-Segal spaces introduced by Dyckerhoff-Kapranov and Galvez-Carrillo-Kock-Tonks.