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arXiv · 1304.6328

Cellular coalgebras over the Barratt-Eccles operad I

Justin R. Smith
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Abstract

This paper considers a class of coalgebras over the Barratt-Eccles operad and shows that they classify Z-completions of pointed, reduced simplicial sets. As a consequence, they encapsulate the homotopy types of nilpotent simplicial sets. This result is a direct generalization of Quillen's result characterizing rational homotopy types via cocommutative coalgebras.

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Justin R. Smith. 2013-04-23. Cellular coalgebras over the Barratt-Eccles operad I. https://arxiv.org/abs/1304.6328

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