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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