Dendroidal Segal spaces and infinity-operads

Denis-Charles Cisinski (1) , Ieke Moerdijk (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Mathematisch Instituut

We introduce the dendroidal analogs of the notions of complete Segal space and of Segal category, and construct two appropriate model categories for which each of these notions corresponds to the property of being fibrant. We prove that these two model categories are Quillen equivalent to each other, and to the monoidal model category for infinity-operads which we constructed in an earlier paper. By slicing over the monoidal unit objects in these model categories, we derive as immediate corollaries the known comparison results between Joyal's quasi-categories, Rezk's complete Segal spaces, and Segal categories.

Domaines: Catégories et ensembles [math.CT]; Topologie algébrique [math.AT]

Denis-Charles Cisinski, Ieke Moerdijk. Dendroidal Segal spaces and infinity-operads. Journal of topology, 2013, 6 (3), pp.675-704. ⟨10.1112/jtopol/jtt004⟩. ⟨hal-00529714⟩