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Dwyer–Kan homotopy theory for cyclic operads

Published online by Cambridge University Press:  14 January 2021

Gabriel C. Drummond-Cole
Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang37673, Republic of Korea (
Philip Hackney
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA (


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.

Research Article
Copyright © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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