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2019 Higher cyclic operads
Philip Hackney, Marcy Robertson, Donald Yau
Algebr. Geom. Topol. 19(2): 863-940 (2019). DOI: 10.2140/agt.2019.19.863

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 Ξ of trees, which carries a tight relationship to the Moerdijk–Weiss category of rooted trees Ω. We prove a nerve theorem exhibiting colored cyclic operads as presheaves on Ξ 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.

Citation

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Philip Hackney. Marcy Robertson. Donald Yau. "Higher cyclic operads." Algebr. Geom. Topol. 19 (2) 863 - 940, 2019. https://doi.org/10.2140/agt.2019.19.863

Information

Received: 10 October 2017; Revised: 9 June 2018; Accepted: 2 August 2018; Published: 2019
First available in Project Euclid: 19 March 2019

zbMATH: 07075116
MathSciNet: MR3924179
Digital Object Identifier: 10.2140/agt.2019.19.863

Subjects:
Primary: 05C05, 18D50, 55P48, 55U35
Secondary: 18G30, 18G55, 37E25, 55U10

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 2 • 2019
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