## Algebraic & Geometric Topology

### Spectra associated to symmetric monoidal bicategories

Angélica M Osorno

#### Abstract

We show how to construct a $Γ$–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 $Γ$–category construction for a permutative category. As an example, we use this machinery to construct a delooping of the $K$–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].

#### Article information

Source
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 307-342.

Dates
Revised: 21 November 2011
Accepted: 28 November 2011
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715341

Digital Object Identifier
doi:10.2140/agt.2012.12.307

Mathematical Reviews number (MathSciNet)
MR2916278

Zentralblatt MATH identifier
1276.18006

#### Citation

Osorno, Angélica M. Spectra associated to symmetric monoidal bicategories. Algebr. Geom. Topol. 12 (2012), no. 1, 307--342. doi:10.2140/agt.2012.12.307. https://projecteuclid.org/euclid.agt/1513715341

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