Homology, Homotopy and Applications

Volume 25 (2023)

Number 1

Multicategories model all connective spectra

Pages: 147 – 172

DOI: https://dx.doi.org/10.4310/HHA.2023.v25.n1.a8

Authors

Niles Johnson (Department of Mathematics, Ohio State University, Newark, Ohio, U.S.A.)

Donald Yau (Department of Mathematics, Ohio State University, Newark, Ohio, U.S.A.)

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.

Keywords

multicategory, connective spectrum, permutative category

2010 Mathematics Subject Classification

55P42

Received 17 November 2021

Received revised 10 March 2022

Accepted 17 March 2022

Published 22 March 2023