nLab model structure on strict omega-groupoids

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Note: model structure on strict omega-groupoids and model structure on strict omega-groupoids both redirect for "model structure on strict ∞-groupoids".
Contents

Context

Model category theory

model category, model ∞ \infty -category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for ∞\infty-groupoids

for ∞-groupoids

for equivariant ∞\infty-groupoids

for rational ∞\infty-groupoids

for rational equivariant ∞\infty-groupoids

for nn-groupoids

for ∞\infty-groups

for ∞\infty-algebras

general ∞\infty-algebras

specific ∞\infty-algebras

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 ∞-categories.

References

The model structure was given in

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.

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

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