Models for cyclic infinity operads

2025/06/18 by Brandon Doherty, Philip Hackney, Doherty, Brandon +1 · 1 citation
Mathematics · Medicine · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Pituitary Gland Disorders and Treatments

paper · pdf · doi:10.48550/arxiv.2506.15622

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 ∞-operads. We infer similar statements for planar cyclic ∞-operads, providing the model-categorical foundation needed to complete Walde's program on the relationship between cyclic 2-Segal spaces and planar cyclic ∞-operads.

Citations

• Profinite completions of topological operads
• Rigidification of dendroidal infinity-operads
• Homotopy-coherent algebra via Segal conditions
• A note on the model (co-)slice categories
• On the equivalence between Lurie's model and the dendroidal model for infinity-operads
• Higher Topos Theory
• A model category structure on the category of simplicial categories

Cited by

• Grothendieck--Teichmüller Symmetries of Cyclic Operads and Tangles

Related

• Dendroidal Segal spaces and infinity-operads
• Cyclic Segal Spaces
• On the equivalence between Lurie's model and the dendroidal model for infinity-operads
• Closed dendroidal sets and unital operads
• A folk Quillen model structure for operads