#
nLab

model structure for weak complicial sets

Contents
### 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 $(\infty,1)$-categories

## Model structures

### for $\infty$-groupoids

for ∞-groupoids

### for rational $\infty$-groupoids

### for $n$-groupoids

### for $\infty$-groups

### for $\infty$-algebras

#### general

#### specific

### 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

# Contents

## Idea

The notion of weak complicial set is a model for (the omega-nerve of) the notion of weak ∞-category. The **model structure for weak $\omega$-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 $\omega$-categories.

## References

Section 6 of

Last revised on November 10, 2014 at 20:41:13.
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