Cellular coalgebras over the Barratt-Eccles operad I

2013/04/23 by Justin R Smith, Smith, Justin R.
Mathematics · #18D50 #55P15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1304.6328

openalex publication_date 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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