## Dwyer-Kan homotopy theory for cyclic operads

### Philip Hackney – 16 May 2018

The Bergner model structure on categories enriched in simplicial sets admits an extension to the Cisinski-Moerdijk model structure on (colored) operads enriched in simplicial sets. The first is a model for (oo,1)-categories, while the second is a model for oo-operads. The weak equivalences in both are called Dwyer-Kan equivalences, that is, maps which are locally Kan equivalences of simplicial sets and which induce equivalences on the underlying categories. Gabriel C. Drummond-Cole and I have shown that there is a corresponding model structure for the category of cyclic operads enriched in simplicial sets.

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