Higher cyclic operads
Autor(en): | Hackney, Philip Robertson, Marcy Yau, Donald |
Stichwörter: | CATEGORIES; DENDROIDAL SETS; Mathematics; MULTICATEGORIES; NOTION; SPACES; THEOREM | Erscheinungsdatum: | 2019 | Herausgeber: | GEOMETRY & TOPOLOGY PUBLICATIONS | Journal: | ALGEBRAIC AND GEOMETRIC TOPOLOGY | Volumen: | 19 | Ausgabe: | 2 | Startseite: | 863 | Seitenende: | 940 | Zusammenfassung: | 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. |
ISSN: | 14722739 | DOI: | 10.2140/agt.2019.19.863 |
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