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model structure for dendroidal Cartesian fibrations

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Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (∞,1)-categories

Model structures

for ∞-groupoids

for ∞-groupoids

for n-groupoids

for ∞-groups

for ∞-algebras

general

specific

for stable/spectrum objects

for (∞,1)-categories

for stable (∞,1)-categories

for (∞,1)-operads

for (n,r)-categories

for (∞,1)-sheaves / ∞-stacks

Higher algebra

higher algebra

universal algebra

Algebraic theories

Algebras and modules

Higher algebras

Model category presentations

Geometry on formal duals of algebras

Theorems

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)
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