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dc.contributor.authorCurien, Pierre Louisen
dc.contributor.authorObradović, Jovanaen
dc.date.accessioned2020-05-18T13:06:57Z-
dc.date.available2020-05-18T13:06:57Z-
dc.date.issued2020-02-01en
dc.identifier.issn0927-2852en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/2738-
dc.description.abstractIn this paper, we introduce a notion of categorified cyclic operad for set-based cyclic operads with symmetries. Our categorification is obtained by relaxing defining axioms of cyclic operads to isomorphisms and by formulating coherence conditions for these isomorphisms. The coherence theorem that we prove has the form “all diagrams of canonical isomorphisms commute”. Our coherence results come in two flavours, corresponding to the “entries-only” and “exchangeable-output” definitions of cyclic operads. Our proof of coherence in the entries-only style is of syntactic nature and relies on the coherence of categorified non-symmetric operads established by Došen and Petrić. We obtain the coherence in the exchangeable-output style by “lifting” the equivalence between entries-only and exchangeable-output cyclic operads, set up by the second author. Finally, we show that a generalization of the structure of profunctors of Bénabou provides an example of categorified cyclic operad, and we exploit the coherence of categorified cyclic operads in proving that the Feynman category for cyclic operads, due to Kaufmann and Ward, admits an odd version.en
dc.publisherSpringer Link-
dc.relation.ispartofApplied Categorical Structuresen
dc.subjectCategorification | Coherence | Cyclic operadsen
dc.titleCategorified Cyclic Operadsen
dc.typeArticleen
dc.identifier.doi10.1007/s10485-019-09569-7en
dc.identifier.scopus2-s2.0-85066800407en
dc.relation.firstpage59en
dc.relation.lastpage112en
dc.relation.issue1en
dc.relation.volume28en
dc.description.rankM23-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
item.grantfulltextnone-
crisitem.author.orcid0000-0001-7407-4668-
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