The diagonal of cellular spaces and effective algebro-homotopical constructions

2021/11/11 by Anibal M. Medina-Mardones, Medina-Mardones, Anibal M. · 2 citations
Mathematics · #18M70 #18M85 #18N40 #55G05 #55G30 #55U15 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2111.06164

openalex publication_date 2021/11/11 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this survey article we discuss certain homotopy coherent enhancements of the coalgebra structure on cellular chains defined by an approximation to the diagonal. Over the rational numbers, C_∞-coalgebra structures control the \mathbb Q-complete homotopy theory of spaces, and over the integers, E_∞-coalgebras provide an appropriate setting to model the full homotopy category. Effective constructions of these structures, the focus of this work, carry geometric and combinatorial information which has found applications in various fields including deformation theory, higher category theory, and condensed matter physics.

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