# nLab model structure for dendroidal Cartesian fibrations

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

#### Higher algebra

higher algebra

universal 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

Last revised on March 7, 2012 at 10:39:14. See the history of this page for a list of all contributions to it.