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On the equivalence between Lurie's model and the dendroidal model for\n infinity-operads

2013/05/15 by Gijs Heuts, Heuts, Gijs, Vladimir Hinich +3 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1305.3658

openalex publication_date 2013/05/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We compare two approaches to the homotopy theory of infinity-operads. One of\nthem, the theory of dendroidal sets, is based on an extension of the theory of\nsimplicial sets and infinity-categories which replaces simplices by trees. The\nother is based on a certain homotopy theory of marked simplicial sets over the\nnerve of Segal's category Gamma. In this paper we prove that for operads\nwithout constants these two theories are equivalent, in the precise sense of\nthe existence of a zig-zag of Quillen equivalences between the respective model\ncategories.\n

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