Spectra associated to symmetric monoidal bicategories

Details Spectra associated to symmetric monoidal bicategories Spectra associated to symmetric monoidal bicategories

2010-05-12

arxiv.org/abs/1005.2227v2

Mathematics

Algebraic Topology

27 pages; originally submitted as: "An Infinite Loop Space Structure for K-theory of Bimonoidal Categories", this version has

Scientific paper

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 bipermutative category. As an example, we use this machinery to construct a delooping of the K-theory of a bimonoidal category as defined by Baas-Dundas-Rognes.

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