An Inverse K-Theory Functor

TL;DR

This paper introduces a new construction of permutative categories from Gamma-spaces to re-prove Thomason's theorem relating symmetric monoidal categories and connective spectra, providing a novel perspective in algebraic K-theory.

Contribution

It presents a new method to construct permutative categories from Gamma-spaces, offering an alternative proof of Thomason's theorem and its variant.

Findings

Re-proves Thomason's theorem using the new construction

Provides a non-completed variant of the theorem

Establishes a new link between Gamma-spaces and permutative categories

Abstract

Thomason showed that the K-theory of symmetric monoidal categories models all connective spectra. This paper describes a new construction of a permutative category from a Gamma-space, which is then used to re-prove Thomason's theorem and a non-completed variant.