Multicategories Model All Connective Spectra

TL;DR

This paper demonstrates that a specific free construction from multicategories to permutative categories induces an equivalence of homotopy theories, extending Thomason's result that permutative categories model all connective spectra.

Contribution

It establishes a new equivalence between multicategories and permutative categories in homotopy theory, broadening the understanding of connective spectra modeling.

Findings

The free construction induces an equivalence of homotopy theories.

Extends Thomason's result to a broader categorical context.

Shows that multicategories can model all connective spectra.

Abstract

There is a free construction from multicategories to permutative categories, left adjoint to the endomorphism multicategory construction. The main result shows that these functors induce an equivalence of homotopy theories. This result extends a similar result of Thomason, that permutative categories model all connective spectra.