Spectra associated to symmetric monoidal bicategories
Algebraic Topology
2013-08-29 v2 Category Theory
K-Theory and Homology
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.
Cite
@article{arxiv.1005.2227,
title = {Spectra associated to symmetric monoidal bicategories},
author = {Angélica Osorno},
journal= {arXiv preprint arXiv:1005.2227},
year = {2013}
}
Comments
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