Dendroidal sets as models for homotopy operads

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

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Mathematisch Instituut

The homotopy theory of infinity-operads is defined by extending Joyal's homotopy theory of infinity-categories to the category of dendroidal sets. We prove that the category of dendroidal sets is endowed with a model category structure whose fibrant objects are the infinity-operads (i.e. dendroidal inner Kan complexes). This extends the theory of infinity-categories in the sense that the Joyal model category structure on simplicial sets whose fibrant objects are the infinity-categories is recovered from the model category structure on dendroidal sets by simply slicing over the point.

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

Denis-Charles Cisinski, Ieke Moerdijk. Dendroidal sets as models for homotopy operads. Journal of topology, 2011, 4 (2), pp.257-299. ⟨10.1112/jtopol/jtq039⟩. ⟨hal-00440931⟩