Dwyer–Kan homotopy theory for cyclic operads. Issue 1 (14th February 2021)

• Record Type: Journal Article
• Authors: Drummond-Cole, Gabriel C.; Hackney, Philip
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 64:Issue 1(2021)
• Page Start: 29
• Page End: 58
• Publication Date: 2021-02-14
• Subjects: cyclic operad, -- Quillen model category, -- coloured operad, -- adjoint functor, -- Dwyer–Kan equivalence; 55P48, -- 55U35, -- 18D50, -- 18D20; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091520000267
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We introduce a general definition for coloured cyclic operads over a symmetric monoidal ground category, which has several appealing features. The forgetful functor from coloured cyclic operads to coloured 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 coloured operads enriched in simplicial sets to the category of coloured cyclic operads enriched in simplicial sets.