Coalgebras in symmetric monoidal categories of spectra

@article{Peroux2019CoalgebrasIS,
  title={Coalgebras in symmetric monoidal categories of spectra},
  author={Maximilien P'eroux and Brooke E. Shipley},
  journal={Homology, Homotopy and Applications},
  year={2019}
}
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. 
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