We show how to construct a –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 –category construction for a permutative category. As an example, we use this machinery to construct a delooping of the –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].
Angélica M Osorno. "Spectra associated to symmetric monoidal bicategories." Algebr. Geom. Topol. 12 (1) 307 - 342, 2012. https://doi.org/10.2140/agt.2012.12.307