# nLab model structure on strict omega-groupoids

Contents

### Context

#### Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for $\infty$-groupoids

for ∞-groupoids

for equivariant $\infty$-groupoids

for rational $\infty$-groupoids

for rational equivariant $\infty$-groupoids

for $n$-groupoids

for $\infty$-groups

for $\infty$-algebras

general $\infty$-algebras

specific $\infty$-algebras

for stable/spectrum objects

for $(\infty,1)$-categories

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

for $(\infty,1)$-operads

for $(n,r)$-categories

for $(\infty,1)$-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 ∞-categories.

## References

The model structure was given in

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.

Last revised on January 20, 2015 at 12:57:26. See the history of this page for a list of all contributions to it.