nLab tree category




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


Finite planar level tree

(… ) see Berger

Finite symmetric rooted trees

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

The objects of Ω\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 Ω\Omega is a morphism of the corresponding operads.

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

Operadic structure

Ω\Omega can be turned into a (symmetric) operad by grafting trees.

Dendroidal sets

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


Last revised on October 26, 2019 at 14:38:42. See the history of this page for a list of all contributions to it.