Geodesic
Monoid-like definitions of cyclic operad
Theory and applications of categories, Tome 32 (2017), pp. 396-436.

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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.
Publié le :
Classification : 18D50, 18D10, 05A99
Keywords: operads, cyclic operads, species of structures, monoid, microcosm principle 
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     author = {Jovana Obradovic},
     title = {Monoid-like definitions of cyclic operad},
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     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a11/}
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Jovana Obradovic. Monoid-like definitions of cyclic operad. Theory and applications of categories, Tome 32 (2017), pp. 396-436. http://geodesic.mathdoc.fr/item/TAC_2017_32_a11/