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The dendroidal category is a test category

Published online by Cambridge University Press:  26 April 2018

DIMITRI ARA ,
DENIS-CHARLES CISINSKI  and
IEKE MOERDIJK
DIMITRI ARA
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France. e-mail: [email protected]
DENIS-CHARLES CISINSKI
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Deutschland. e-mail: [email protected]
IEKE MOERDIJK
Affiliation:
Department of Mathematics, Utrecht University, PO BOX 80.010, 3508 TA Utrecht, The Netherlands. e-mail: [email protected]
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 1 , July 2019 , pp. 107 - 121
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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