Cyclic dendroidal sets and cyclic dendroidal spaces admit model structures for cyclic quasi-operads and complete Segal spaces, both Quillen equivalent to simplicial cyclic operads.
Bergner, A model category structure on the category of simplicial categories, Trans
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Models for cyclic infinity operads
Cyclic dendroidal sets and cyclic dendroidal spaces admit model structures for cyclic quasi-operads and complete Segal spaces, both Quillen equivalent to simplicial cyclic operads.