# nLab Cartesian fibration of dendroidal sets

### Context

#### Higher algebra

higher algebra

universal algebra

## Theorems

#### Higher category theory

higher category theory

# 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.

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## Properties

### Relation to $\infty$-algebra

Let $P$ 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 $P$ are equivalent to ∞-algebras over $P$ in (∞,1)Cat:

$coCart_P \simeq Alg_P(Cat_{(\infty,1)}) \,.$

This is (Heuts, theorem 0.1).

## References

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