TY - JOUR
T1 - The dendroidal category is a test category
AU - Ara, Dimitri
AU - Cisinski, Denis Charles
AU - Moerdijk, Ieke
PY - 2019/7/1
Y1 - 2019/7/1
N2 - We prove that the category of trees Ω 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.
AB - We prove that the category of trees Ω 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.
UR - http://www.scopus.com/inward/record.url?scp=85046035155&partnerID=8YFLogxK
U2 - 10.1017/S030500411800021X
DO - 10.1017/S030500411800021X
M3 - Article
AN - SCOPUS:85046035155
SN - 0305-0041
VL - 167
SP - 107
EP - 121
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 1
ER -