on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
For the -truncation of the Theta-category, an -cellular set, hence a presheaf on , may be viewed as a collection of n-morphisms of an “-graph” underlying an (∞,n)-category. The model structure on cellular sets (Ara) models -categories this way. This model is referred to as n-quasicategories.
Let be the Theta category restricted to -cells. The model structure on cellular sets is the Cisinski model structure on the category of presheaves defined by the following localizer: (…)
In (Ara) the fibrant objects in this model structure are called -quasi-categories, see Relation to quasi-categories below.
For we have is the simplex category; and the model structure on 1-cellular sets reproduces the model structure for quasi-categories. (Ara, theorem 5.26)
The model structure on -cellular sets is Quillen equivalent to that ∞-n spaces. (Ara, theorem 7.4).
Last revised on October 8, 2013 at 20:35:15. See the history of this page for a list of all contributions to it.