Monoid-like definitions of cyclic operad

Jovana Obradovic 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
Inria de Paris, CNRS - Centre National de la Recherche Scientifique, UPD7 - Université Paris Diderot - Paris 7, PPS - Preuves, Programmes et Systèmes
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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Submitted on : Monday, January 21, 2019 - 9:40:31 AM
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Jovana Obradovic. Monoid-like definitions of cyclic operad. Theory and Applications of Categories, Mount Allison University, 2017. ⟨hal-01987321⟩

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