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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Segal-type algebraic models of $n$–types

David Blanc and Simona Paoli

Algebraic & Geometric Topology 14 (2014) 3419–3491
Abstract

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 (k1)–connected n–types.

Keywords
$n$–type, $n$–fold groupoid, weakly globular, algebraic model
Mathematical Subject Classification 2000
Primary: 55S45
Secondary: 18G50, 18B40
References
Publication
Received: 6 September 2013
Revised: 20 February 2014
Accepted: 13 March 2014
Published: 15 January 2015
Authors
David Blanc
Department of Mathematics
University of Haifa
31905 Haifa
Israel
Simona Paoli
Department of Mathematics
University of Leicester
Leicester LE1 7RH
UK