Spectra associated to symmetric monoidal bicategories

Osorno, Angélica M

doi:10.2140/agt.2012.12.307

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Spectra associated to symmetric monoidal bicategories

Angélica M Osorno

Algebraic & Geometric Topology 12 (2012) 307–342

DOI: 10.2140/agt.2012.12.307

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].

Keywords

symmetric monoidal bicategory, spectra, $K$–theory

Mathematical Subject Classification 2010

Primary: 18D05, 55B20, 55P42

Secondary: 19D23, 55N15

References

Publication

Received: 8 December 2010

Revised: 21 November 2011

Accepted: 28 November 2011

Published: 12 March 2012

Authors

Angélica M Osorno
Department of Mathematics University of Chicago 5734 S University Ave Chicago IL 60637 USA
http://math.uchicago.edu/~aosorno

Volume 12, issue 1 (2012)