nLab
model structure for weak complicial sets

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

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 notion of weak complicial set is a model for (the omega-nerve of) the notion of weak ω-category. The model structure for weak ω\omega-categories is a model category structure on the category of stratified simplicial sets, such that cofibrant-fibrant objects are precisely the weak complicial sets. This model structure may therefore be understood as a presentation of the (∞,1)-category of weak ω\omega-categories.

References

Section 6 of

Revised on November 10, 2014 20:41:13 by Urs Schreiber (86.212.18.175)