Segal-type algebraic models of n–types

Blanc, David¹ ; Paoli, Simona²

¹Department of Mathematics, University of Haifa, 31905 Haifa, Israel
²Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK

Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3419-3491

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.3419

Keywords: $n$–type, $n$–fold groupoid, weakly globular, algebraic model

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