Spectra associated to symmetric monoidal bicategories

Abstract

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.

27 pages; originally submitted as: "An Infinite Loop Space Structure for K-theory of Bimonoidal Categories", this version has essentially the same content, but the organization is different

References in corpus (2)

• Nerves and classifying spaces for bicategories
• Stable bundles over rig categories

Cited by in corpus (4)

• Infinite loop spaces, and coherence for symmetric monoidal bicategories
• The 2-dimensional stable homotopy hypothesis
• Twisted iterated algebraic K-theory and topological T-duality for sphere bundles
• K-theory for 2-categories