Authors: Obradović, Jovana 
Title: Monoid-like definitions of cyclic operad
Journal: Theory and Applications of Categories
Volume: 32
First page: 396
Last page: 436
Issue Date: 13-Mar-2017
Rank: M22
ISSN: 1201-561X
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.
Keywords: Cyclic operads | Microcosm principle | Monoid | Operads | Species of structures
Publisher: R. Rosebrugh

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