Segal-type algebraic models of n–types

David Blanc, Simona Paoli

Research output: Contribution to journalArticlepeer-review


For each n≥1, we introduce two new Segal-type models of n–types of topological spaces: weakly globular n–fold groupoids and their lax version. We show that any n–type can be represented up to homotopy by such models via an explicit algebraic fundamental n–fold groupoid functor. We compare these models to Tamsamani’s weak n–groupoids, and extract from them a model for (k−1)–connected n–types.

Original languageAmerican English
Pages (from-to)3419-3491
Number of pages73
JournalAlgebraic and Geometric Topology
Issue number6
StatePublished - 15 Jan 2015


  • Algebraic model
  • N–fold groupoid
  • N–type
  • Weakly globular

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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