Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general -algebras
specific -algebras
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
The notion of model -category (or model -category, for short) is the -categorification of that of model category.
Where the classical model structure on simplicial sets is an archetypical example of a model category, so simplicial -groupoids (“simplicial spaces”, bisimplicial sets) form an archetypical example of a model -category. In this example, a fundamental application of the theory says, for instance, that geometric realization preserves homotopy pullbacks of homotopy Kan fibrations (see there).
Aaron Mazel-Gee, Model ∞-categories I: some pleasant properties of the ∞-category of simplicial spaces [arXiv:1412.8411]
Aaron Mazel-Gee, Model ∞-categories II: Quillen adjunctions, New York Journal of Mathematics 27 (2021) 508-550. [arXiv:1510.04392, nyjm:27-21]
Aaron Mazel-Gee, Model ∞-categories III: the fundamental theorem, New York Journal of Mathematics 27 (2021) 551-599 [arXiv:1510.04777, nyjm:27-22]
Last revised on October 15, 2023 at 08:39:51. See the history of this page for a list of all contributions to it.