Monoid-like definitions of cyclic operads

Jovana Obradović

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arXiv · 1607.02438

Monoid-like definitions of cyclic operads

Jovana Obradović

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Abstract

Guided by the microcosm principle of Baez-Dolan and by the algebraic definitions of operads of Kelly and Fiore, we introduce two "monoid-like" definitions of cyclic operads, one for the original, "exchangable-output" characterisation of Getzler-Kapranov, and the other for the alternative "entries-only" characterisation, both within the category of Joyal's species of structures. Relying on a result of Lamarche on descent for species, we use these "monoid-like" definitions to prove the equivalence between the "exchangable-output" and "entries-only" points of view on cyclic operads.

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Jovana Obradović. 2016-07-08. Monoid-like definitions of cyclic operads. https://arxiv.org/abs/1607.02438

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