Semistrict models of connected 3-types and Tamsamani's weak 3-groupoids

2006/07/14 by Simona Paoli, Paoli, Simona
Mathematics · #18G50) #55P15 (18D05 #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 #math.AT #math.CT #msc:55P15

paper · pdf · doi:10.48550/arxiv.math/0607330

21 pages

arxiv created 2006/07/14 · openalex publication_date 2006/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Homotopy 3-types can be modelled algebraically by Tamsamani's weak 3-groupoids as well as, in the path-connected case, by cat²-groups. This paper gives a comparison between the two models in the path-connected case. This leads to two different semistrict algebraic models of connected 3-types using the Tamsamani's model. Both are then related to Gray groupoids.

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