nLab
Cartesian fibration of dendroidal sets

Context

Higher algebra

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

The notion of Cartesian fibration of dendroidal sets is the generalization from simplicial sets to dendroidal sets of the notion of Cartesian fibration. Accordingly, it is models the notion of Grothendieck fibration for (∞,1)-operads. Its 1-operadic analog is the notion of fibration of multicategories.

Definition

(…)

Properties

Relation to \infty-algebra

Let PP be an (∞,1)-operad, incarnated as a dendroidal set. For instance the homotopy coherent dendroidal nerve of a topological operad/simplicial operad.

Then coCartesian fibrations over PP are equivalent to ∞-algebras over PP in (∞,1)Cat:

coCart PAlg P(Cat (,1)). coCart_P \simeq Alg_P(Cat_{(\infty,1)}) \,.

This is (Heuts, theorem 0.1).

References

Revised on February 29, 2012 00:18:30 by Urs Schreiber (82.169.65.155)