model category

for ∞-groupoids

# 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 $\omega$-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)