nLab
model structure on strict omega-categories

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

The model structure on strict ω\omega-categories is a model category structure that presentes the (∞,1)-category of strict ω-categories.

It resticts to the model structure on strict ω-groupoids.

These structures also go by the name canonical model structure or folk model structure.

Properties

Observation

Every object is fibrant. The acyclic fibrations are precisely the functors that are k-surjective functors for all kk \in \mathbb{N}.

Theorem

The transferred model structure on StrωGrpd along the forgetful functor

U:StrωGrpdStrωCat U : Str \omega Grpd \to Str \omega Cat

exists and coincides with the model structure on strict ω-groupoids defined in (BrownGolasinski).

This is proven in (AraMetayer).

References

The model structure on strict ω-groupoids was introduced in

The model structure on strict ω\omega-categories was discussed in

Dicussion of cofibrant resolution in this model structure by polygraphs/computad is in

The relation between the model structure on strict ω\omega-categories and that on strict ω\omega-groupoids is established in

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

Revised on September 13, 2014 19:28:15 by Tim Porter (2.26.39.238)