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Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2019

The dendroidal category is a test category

Résumé

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.

Dates et versions

hal-02529301 , version 1 (02-04-2020)

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Dimitri Ara, Denis-Charles Cisinski, Ieke Moerdijk. The dendroidal category is a test category. Mathematical Proceedings of the Cambridge Philosophical Society, 2019, 167 (01), pp.107-121. ⟨10.1017/S030500411800021X⟩. ⟨hal-02529301⟩
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