Models for cyclic infinity operads

Brandon Doherty; Philip Hackney

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arXiv · 2506.15622

Models for cyclic infinity operads

Brandon Doherty·Philip Hackney

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Abstract

We construct model structures on cyclic dendroidal sets and cyclic dendroidal spaces for cyclic quasi-operads and complete cyclic dendroidal Segal spaces, respectively. We show these models are Quillen equivalent to the model structure for simplicial cyclic operads. This answers in the affirmative a question of the second author and Drummond-Cole concerning model structures for cyclic $\infty$-operads. We infer similar statements for planar cyclic $\infty$-operads, providing the model-categorical foundation needed to complete Walde's program on the relationship between cyclic 2-Segal spaces and planar cyclic $\infty$-operads.

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BibTeX RIS

Brandon Doherty, Philip Hackney. 2025-06-18. Models for cyclic infinity operads. https://arxiv.org/abs/2506.15622

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