K-theory for 2-categories

TL;DR

This paper develops a homotopy-theoretic framework connecting symmetric monoidal bicategories with connective spectra, introducing $ ext{Gamma}$-objects in 2-categories and proving strictification results.

Contribution

It establishes an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra, advancing the understanding of higher categorical structures in homotopy theory.

Findings

Equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra

Development of $ ext{Gamma}$-objects in 2-categories

Strictification results for symmetric monoidal bicategories and diagrams of 2-categories

Abstract

We establish an equivalence of homotopy theories between symmetric monoidal bicategories and connective spectra. For this, we develop the theory of $\Gamma$-objects in 2-categories. In the course of the proof we establish strictfication results of independent interest for symmetric monoidal bicategories and for diagrams of 2-categories.