Spectra associated to symmetric monoidal bicategories

TL;DR

This paper develops a method to construct infinite loop spaces from symmetric monoidal bicategories using Gamma-bicategories, linking to classical Gamma-category constructions and applying it to K-theory delooping.

Contribution

It introduces a new construction of Gamma-bicategories from symmetric monoidal bicategories and relates it to classical Gamma-category methods, with applications to K-theory.

Findings

Classifying space becomes an infinite loop space after group completion.

Establishes a connection between Gamma-bicategories and Gamma-categories.

Provides a delooping of K-theory for bimonoidal categories.

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.