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arXiv · 1611.02591

Higher cyclic operads

Philip Hackney·Marcy Robertson·Donald Yau
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Abstract

We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category $\Xi$ of trees, which carries a tight relationship to the Moerdijk-Weiss category of rooted trees $\Omega$. We prove a nerve theorem exhibiting colored cyclic operads as presheaves on $\Xi$ which satisfy a Segal condition. Finally, we produce a Quillen model category whose fibrant objects satisfy a weak Segal condition, and we consider these objects as an up-to-homotopy generalization of the concept of cyclic operad.

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Philip Hackney, Marcy Robertson, Donald Yau. 2016-11-08. Higher cyclic operads. https://doi.org/10.2140/agt.2019.19.863

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