Dwyer--Kan homotopy theory for cyclic operads

Gabriel C. Drummond-Cole; Philip Hackney

doi:10.1017/s0013091520000267

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arXiv · 1809.06322

Dwyer--Kan homotopy theory for cyclic operads

Gabriel C. Drummond-Cole·Philip Hackney

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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.

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BibTeX RIS

Gabriel C. Drummond-Cole, Philip Hackney. 2018-09-17. Dwyer--Kan homotopy theory for cyclic operads. https://doi.org/10.1017/s0013091520000267

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