Homology, Homotopy and Applications

Volume 21 (2019)

Number 1

Coalgebras in symmetric monoidal categories of spectra

Pages: 1 – 18

DOI: https://dx.doi.org/10.4310/HHA.2019.v21.n1.a1

Authors

Maximilien Péroux (Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Il., U.S.A.)

Brooke Shipley (Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Il., U.S.A.)

Abstract

We show that all coalgebras over the sphere spectrum are cocommutative in the category of symmetric spectra, orthogonal spectra, $\Gamma$-spaces, $\mathcal{W}$-spaces and EKMM $\mathbb{S}$-modules. Our result only applies to these strict monoidal categories of spectra and does not apply to the $\infty$-category setting.

Keywords

homotopy, spectrum, coalgebra, comonoid

2010 Mathematics Subject Classification

16T15, 18D10, 55P42, 55P43

Received 1 August 2017

Received revised 19 February 2018

Published 15 August 2018