Homology, Homotopy and Applications

Volume 13 (2011)

Number 1

The Brown-Golasiński model structure on strict $\infty$-groupoids revisited

Pages: 121 – 142

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n1.a6

Authors

Dimitri Ara (Institut Mathématiques de Jussieu, Université Paris Diderot – Paris 7, Paris, France)

François Métayer (Laboratoire PPS, Université Paris Diderot – Paris 7 & CNRS, Paris, France)

Abstract

We prove that the folk model structure on strict $\infty$-categories transfers to the category of strict $\infty$-groupoids (and more generally to the category of strict $(\infty; n)$-categories), and that the resulting model structure on strict $\infty$-groupoids coincides with the one defined by Brown and Golasiński via crossed complexes.

Keywords

$\infty$-category, $\infty$-groupoid, crossed complex, model category

2010 Mathematics Subject Classification

18D05, 18G55, 55U35

Published 12 July 2011