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 10:38:42. See the history of this page for a list of all contributions to it.