K-theory for 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.

73 pages. Updated to match publication

References in corpus (5)

• Biequivalences in tricategories
• Quasistrict symmetric monoidal 2-categories via wire diagrams
• An Inverse K-Theory Functor
• Bicategorical homotopy pullbacks
• Extending homotopy theories across adjunctions

Cited by in corpus (7)

• The 2-dimensional stable homotopy hypothesis
• Stable Postnikov data of Picard 2-categories
• Coherence for braided and symmetric pseudomonoids
• Multifunctorial Inverse $K$-Theory
• Multicategories Model All Connective Spectra
• 2-categorical opfibrations, Quillen's Theorem B, and $S^{-1}S$
• Multifunctorial $K$-Theory is an Equivalence of Homotopy Theories