model category, model $\infty$-category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$-categories
Model structures
for $\infty$-groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
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
The model structure on strict $\omega$-categories is a model category structure that presentes the (∞,1)-category of strict ∞-categories.
It resticts to the model structure on strict ∞-groupoids.
These structures also go by the name canonical model structure or folk model structure.
Every object is fibrant. The acyclic fibrations are precisely the functors that are k-surjective functors for all $k \in \mathbb{N}$.
The transferred model structure on Str∞Grpd? along the forgetful functor
exists and coincides with the model structure on strict ∞-groupoids defined in (BrownGolasinski).
This is proven in (AraMetayer).
The model structure on strict ∞-groupoids was introduced in
The model structure on strict $\omega$-categories was discussed in
Dicussion of cofibrant resolution in this model structure by polygraphs/computad is in
Francois Métayer, Cofibrant complexes are free (arXiv)
Francois Métayer, Resolutions by polygraphs (tac)
The relation between the model structure on strict $\omega$-categories and that on strict $\omega$-groupoids is established in
Last revised on November 10, 2014 at 20:37:04. See the history of this page for a list of all contributions to it.