Spectra associated to symmetric monoidal bicategories

Abstract

We show how to construct a $\Gamma$–bicategory from a symmetric monoidal bicategory and use that to show that the classifying space is an infinite loop space upon group completion. We also show a way to relate this construction to the classic $\Gamma$–category construction for a permutative category. As an example, we use this machinery to construct a delooping of the $\mathcal{K}$–theory of a rig category as defined by Baas, Dundas and Rognes [London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 18–45].