Monoid-like definitions of cyclic operad

Jovana Obradovic (1, 2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 PI.R2 - Design, study and implementation of languages for proofs and programs

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.

Domaines: Topologie algébrique [math.AT]; Combinatoire [math.CO]; Catégories et ensembles [math.CT]

Jovana Obradovic. Monoid-like definitions of cyclic operad. Theory and Applications of Categories, 2017. ⟨hal-01987321⟩