Dwyer--Kan homotopy theory for cyclic operads

Abstract

We introduce a general definition for colored cyclic operads over a symmetric monoidal ground category, which has several appealing features. The forgetful functor from colored cyclic operads to colored operads has both adjoints, each of which is relatively simple. Explicit formulae for these adjoints allow us to lift the Cisinski--Moerdijk model structure on the category of colored operads enriched in simplicial sets to the category of colored cyclic operads enriched in simplicial sets.

v3: updated numbering of theorem-like environments, subsections, and equations to reflect those in published version. no other changes. v2: final version, four figures added

References in corpus (4)

• A graphical category for higher modular operads
• A criterion for existence of right-induced model structures
• Dwyer-Kan Homotopy Theory of Algebras over Operadic Collections
• Coextension of scalars in operad theory

Cited by in corpus (9)

• A graphical category for higher modular operads
• Modular operads and the nerve theorem
• The 2-Chu-Dialectica construction and the polycategory of multivariable adjunctions
• Graphical combinatorics and a distributive law for modular operads
• Categories of graphs for operadic structures
• Coextension of scalars in operad theory
• LNL polycategories and doctrines of linear logic
• Segal conditions for generalized operads
• *-Autonomous Envelopes and Conservativity