Monoid-like definitions of cyclic operad

Jovana Obradovic

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: operads, cyclic operads, species of structures, monoid, microcosm principle

2010 MSC: 18D50, 18D10, 05A99

Theory and Applications of Categories, Vol. 32, 2017, No. 12, pp 396-436.

Published 2017-03-13.

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