2016/11/30 by Philip Hackney, Marcy Robertson, Donald Yau
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Colored #Cyclic homology #Generalization #Homotopy and Cohomology in Algebraic Topology #Model category #math.AT #math.CT
paper · pdf · doi:10.2140/agt.2019.19.863
published as Algebr. Geom. Topol. 19 (2019) 863-940 · This version has been accepted to AGT. Substantial updates throughout, including an alternative description (suggested by the referee) of the morphisms of $Ξ$, a new appendix, and various other improvements
openalex created_date 2016/11/30 · arxiv created 2018/08/11 · openalex publication_date 2019/03/12 · arxiv updated 2019/03/20 · openalex updated_date 2026/08/05
We introduce a convenient definition for weak cyclic operads, which is based on unrooted trees and Segal conditions. More specifically, we introduce a category [math] of trees, which carries a tight relationship to the Moerdijk–Weiss category of rooted trees [math] . We prove a nerve theorem exhibiting colored cyclic operads as presheaves on [math] 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.