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 | 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. |
Keywords: | Cyclic operads | Microcosm principle | Monoid | Operads | Species of structures | Publisher: | R. Rosebrugh |
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