Dendroidal sets as models for homotopy operads

Details Dendroidal sets as models for homotopy operads Dendroidal sets as models for homotopy operads

2009-02-11

arxiv.org/abs/0902.1954v1

Journal of Topology 4 (2011), no. 2, 257-299

Mathematics

Category Theory

Scientific paper

10.1112/jtopol/jtq039

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.

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