Segal-type algebraic models of n–types

Blanc, David; Paoli, Simona

doi:10.2140/agt.2014.14.3419

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Segal-type algebraic models of $n$–types

David Blanc and Simona Paoli

Algebraic & Geometric Topology 14 (2014) 3419–3491

DOI: 10.2140/agt.2014.14.3419

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 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.

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

Volume 14, issue 6 (2014)