#### Volume 12, issue 1 (2012)

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Spectra associated to symmetric monoidal bicategories

### Angélica M Osorno

Algebraic & Geometric Topology 12 (2012) 307–342
##### 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 $\mathsc{K}$–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].

##### Keywords
symmetric monoidal bicategory, spectra, $K$–theory
##### Mathematical Subject Classification 2010
Primary: 18D05, 55B20, 55P42
Secondary: 19D23, 55N15