Geodesic
Twisted arrow categories, operads and Segal conditions
Theory and applications of categories, Tome 38 (2022), pp. 595-660

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We introduce twisted arrow categories of operads and of algebras over operads. Up to equivalence of categories, the simplex category Δ, Segal's category Γ, Connes cyclic category Λ, Moerdijk-Weiss dendroidal category Ω, and categories similar to graphical categories of Hackney-Robertson-Yau are twisted arrow categories of symmetric or cyclic operads. Twisted arrow categories of operads admit Segal presheaves and 2-Segal presheaves, or decomposition spaces. Twisted arrow category of an operad P is the (∞, 1)-localization of the corresponding category Ω/P by the boundary preserving morphisms. Under mild assumptions, twisted arrow categories of operads, and closely related universal enveloping categories, are generalized Reedy. We also introduce twisted arrow operads, which are related to Baez-Dolan plus construction.

Publié le :
Classification : 18F20, 18N70, 55U35, 55U40, 18M85
Keywords: Segal conditions, 2-Segal spaces, operads, dendroidal sets 
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     author = {Sergei Burkin},
     title = {Twisted arrow categories, operads and {Segal} conditions},
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     volume = {38},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a15/}
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Sergei Burkin. Twisted arrow categories, operads and Segal conditions. Theory and applications of categories, Tome 38 (2022), pp. 595-660. http://geodesic.mathdoc.fr/item/TAC_2022_38_a15/