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cyclic operad

Proceedings of the Edinburgh Mathematical Society (1)

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Dwyer–Kan homotopy theory for cyclic operads
Part of
Gabriel C. Drummond-Cole, Philip Hackney
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 1 / February 2021

Published online by Cambridge University Press:

14 January 2021, pp. 29-58
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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.