#### Volume 14, issue 6 (2014)

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Segal-type algebraic models of $n$–types

### David Blanc and Simona Paoli

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

For each $n\ge 1$, 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 $\left(k-1\right)$–connected $n$–types.

##### Keywords
$n$–type, $n$–fold groupoid, weakly globular, algebraic model
##### Mathematical Subject Classification 2000
Primary: 55S45
Secondary: 18G50, 18B40