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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 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