Modelling Connective Spectra via Multicategories

TL;DR

This paper develops a model structure on based multicategories to better understand connective spectra, extending Thomason's theorem and showing symmetric monoidal groupoids suffice for modeling spectra.

Contribution

It introduces a new model structure on based multicategories that lifts Thomason's theorem to a categorical framework for connective spectra.

Findings

A model structure on based multicategories is established.

The model structure lifts to a semi-model structure on multicategories.

Symmetric monoidal groupoids suffice to model connective spectra.

Abstract

We put a model structure on a full subcategory of based multicategories in which the weak equivalences are created by the K-theory functor of Elmendorf-Mandell, providing a model categorical lift of Thomason's theorem on the modeling of connective spectra by symmetric monoidal categories. We note that this lifts to a semi-modelstructure on based multicategories itself. As a corollary we show that to model connective spectra up to stable equivalence it suffices to restrict to symmetric monoidal groupoids.