# nLab model structure on cubical presheaves

Contents

### Context

#### Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for $\infty$-groupoids

for ∞-groupoids

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

#### $(\infty,1)$-Topos Theory

(∞,1)-topos theory

## Constructions

structures in a cohesive (∞,1)-topos

# Contents

## Idea

Given a site, there is a model category structure on the category of cubical objects in the presheaf topos over that site, hence on the category of cubical set-valued presheaves, such that at least the corresponding homotopy category is equivalent to that of the corresponding local model structure on simplicial presheaves (Jardine 03, theorem 71) (the latter being known to present the (infinity,1)-topos over the given site).

## References

Created on April 16, 2015 at 05:23:54. See the history of this page for a list of all contributions to it.