nLab
model structure on strict omega-groupoids

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

Contents

Idea

There is a cofibrantly generated (“folk”) model structure on the category of strict ∞-groupoids, equivalently that of crossed complexes.

It is the transferred model structure along the forgetful functor of the model structure on strict ω-categories.

References

The model structure was given in

  • Ronnie Brown, Marek Golasinski; A model structure for the homotopy theory of crossed complexes (numdam) Cahiers Topologie Géom. Différentielle 30 (1989) 61-82.

The relation to the model structure on strict ω\omega-categories was established in

  • Dimitri Ara, Francois Metayer, The Brown-Golasinski model structure on \infty-groupoids revisited (pdf) Homology, Homotopy Appl. 13 (2011), no. 1, 121–142.

Revised on January 24, 2012 19:44:05 by Ronnie Brown (217.43.153.23)