# Contents

## Idea

The simplex category may be regarded as the category of all linear directed graphs. The tree category generalizes this to directed rooted trees.

## Definition

(… ) see Berger

### Finite symmetric rooted trees

We define the category $\Omega$ finite symmetric rooted trees.

The objects of $\Omega$ are non-empty non-planar trees with specified root.

Each such tree may naturally be regarded as specifying an (colored) symmetric operad with one color per edge of the tree. A morphism of trees in $\Omega$ is a morphism of the corresponding operads.

As such, $\Omega$ is by construction a full subcategory of that of symmetric operads enriched over Set.

## Dendroidal sets

A presheaf on $\Omega$ is a dendroidal set, a generalization of a simplicial set.

## References

Revised on November 20, 2012 15:11:21 by Stephan Alexander Spahn (92.105.200.182)