#
nLab

model structure for dendroidal Cartesian fibrations

### Context

#### 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 $n$-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

#### Higher algebra

# Contents

## Idea

The *model structure for dendroidal (co)Cartesian fibrations* is an operadic analog of the *model structure for Cartesian fibrations*. Its fibrant objects are (co)Cartesian fibrations of dendroidal sets. These in turn model (Grothendieck-)fibrations of (∞,1)-operads.

In particular, over the terminal object, the E-∞ operad, this is a model for the collection symmetric monoidal (∞,1)-categories. Over an arbitrary (∞,1)-operad, this is a model for the (∞,1)-category OMon(∞,1)Cat of O-monoidal (∞,1)-categories?.

For an overview of models for (∞,1)-operads see *table - models for (infinity,1)-operads*.

## References

The model structure for dendroidal Cartesian fibrations is due to

Its further localization to the model structure for dendroidal left fibrations is discussed in

Revised on March 7, 2012 10:39:14
by

Urs Schreiber
(82.169.65.155)