Algebraic & Geometric Topology

Spectra associated to symmetric monoidal bicategories

Angélica M Osorno

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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
Received: 8 December 2010
Revised: 21 November 2011
Accepted: 28 November 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Subjects
Primary: 18D05: Double categories, 2-categories, bicategories and generalizations 55B20 55P42: Stable homotopy theory, spectra
Secondary: 19D23: Symmetric monoidal categories [See also 18D10] 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}

Keywords
symmetric monoidal bicategory spectra $K$–theory

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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