English

The dendroidal category is a test category

Algebraic Topology 2020-09-09 v2 Category Theory

Abstract

We prove that the category of trees Ω\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.

Keywords

Cite

@article{arxiv.1703.07098,
  title  = {The dendroidal category is a test category},
  author = {Dimitri Ara and Denis-Charles Cisinski and Ieke Moerdijk},
  journal= {arXiv preprint arXiv:1703.07098},
  year   = {2020}
}

Comments

15 pages, v2: minor modifications, final version

R2 v1 2026-06-22T18:52:08.821Z