Topology Seminar: An infinite loop space machine for symmetric monoidal 2-categories

In recent work of Baas-Dundas-Richter-Rognes, the authors prove that the classifying space of 2-vector bundles, K(Vect) is equivalent to the algebraic K-theory of the connective K-theory spectrum ku. In this talk we will show that K(Vect) is the group completion of the classifying space of the 2-category of 2-vector spaces, which is a symmetric monoidal 2-category. We will explain how to use the symmetric monoidal structure to produce a $\Gamma$-2-category, which will give an infinite loop space structure on K(Vect). Then we will show that the equivalence of BDRR is a map of infinite loop spaces.