Categorified cyclic operads
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00521874" target="_blank" >RIV/67985840:_____/20:00521874 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10485-019-09569-7" target="_blank" >https://doi.org/10.1007/s10485-019-09569-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10485-019-09569-7" target="_blank" >10.1007/s10485-019-09569-7</a>
Alternative languages
Result language
angličtina
Original language name
Categorified cyclic operads
Original language description
In 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Categorical Structures
ISSN
0927-2852
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
1
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
54
Pages from-to
59-112
UT code for WoS article
000511930300002
EID of the result in the Scopus database
2-s2.0-85066800407