Tensor 2-categories of Hall modules

Tensor 2-categories are expected to play a fundamental role in 4D quantum topology. The study of tensor 2-categories is still in its early stages, especially when compared to the vast literature developed for tensor categories over the last few decades. In particular, the supply of examples is limited.

In this talk I will present an approach to constructing a wide variety of tensor 2-categories via categorified Hall algebras. More specifically, 2-Segal spaces provide a simplicial framework for unifying the various flavours of Hall algebra constructions. I will describe how to use the theory of 2-Segal spaces to construct categorical Hopf algebras, whose modules form tensor 2-categories.