# The dendroidal category is a test category

## TL;DR

This paper proves that the category of trees is a test category, establishing the dendroidal sets as a model category Quillen-equivalent to spaces, with an explicit localization of the operadic model structure.

## Contribution

It demonstrates that the category of trees is a test category and constructs a model structure on dendroidal sets explicitly related to operadic models.

## Key findings

- Category of trees is a test category.
- Dendroidal sets form a model category Quillen-equivalent to spaces.
- Explicit localization of the operadic model structure achieved.

## Abstract

We prove that the category of trees $\Omega$ is a test category in the sense of Grothendieck. This implies that the category of dendroidal sets is endowed with the structure of a model category Quillen-equivalent to spaces. We show that this model category structure, up to a change of cofibrations, can be obtained as an explicit left Bousfield localisation of the operadic model category structure.