English

Segal-type algebraic models of n-types

Algebraic Topology 2015-05-27 v3 Category Theory

Abstract

For each n\geq 1 we introduce two new Segal-type models of n-types of topological spaces: weakly globular n-fold groupoids, and a lax version of these. 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

Keywords

Cite

@article{arxiv.1204.5101,
  title  = {Segal-type algebraic models of n-types},
  author = {David Blanc and Simona Paoli},
  journal= {arXiv preprint arXiv:1204.5101},
  year   = {2015}
}

Comments

Added index of terminology and notation. Minor amendments and added details is some definitions and proofs. Some typos corrected

R2 v1 2026-06-21T20:53:32.620Z