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arXiv · 1708.02592

Coalgebras in symmetric monoidal categories of spectra

Maximilien Péroux·Brooke Shipley
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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.

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Maximilien Péroux, Brooke Shipley. 2017-08-08. Coalgebras in symmetric monoidal categories of spectra. https://arxiv.org/abs/1708.02592

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