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Higher cyclic
operads
Philip Hackney, Marcy Robertson and Donald Yau |
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Algebraic & Geometric Topology 19 (2019) 863–940
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Abstract |
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We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category of trees, which carries a tight relationship to the Moerdijk–Weiss category of rooted trees . We prove a nerve theorem exhibiting colored cyclic operads as presheaves on 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. |
Keywords
cyclic operad, dendroidal set, Quillen model category,
Reedy category
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Mathematical Subject Classification 2010
Primary: 05C05, 18D50, 55P48, 55U35
Secondary: 37E25, 55U10, 18G30, 18G55
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References |
Publication
Received: 10 October 2017
Revised: 9 June 2018
Accepted: 2 August 2018
Published: 12 March 2019
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Authors |
| Philip Hackney | ||
| Institut für Mathematik Universität Osnabrück Osnabrück Germany |
Max-Planck-Institut für
Mathematik Bonn Germany |
Department of Mathematics University of Louisiana at Lafayette Lafayette, LA United States |
| http://phck.net | ||
| Marcy Robertson | ||
| School of Mathematics and
Statistics University of Melbourne Melbourne Victoria Australia |
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| Donald Yau | ||
| Department of Mathematics The Ohio State University at Newark Newark, OH United States |
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