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

Dimitri Ara (1) , François Métayer (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 PPS - Preuves, Programmes et Systèmes

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 Golasinski via crossed complexes.

Mots clés: $\infty$-category; $\infty$-groupoid; crossed complex; model category

Domaines: Catégories et ensembles [math.CT]; Topologie algébrique [math.AT]

Dimitri Ara, François Métayer. The Brown-Golasinski model structure on strict $\infty$-groupoids revisited. Homology, Homotopy and Applications, 2011, 13 (1), pp.121-142. ⟨hal-00525842v2⟩