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The dendroidal category is a test category

Ara, Dimitri ; Cisinski, Denis-Charles ; Moerdijk, Ieke


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.

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