English

Monoid-like definitions of cyclic operads

Category Theory 2017-04-26 v2

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

Cite

@article{arxiv.1607.02438,
  title  = {Monoid-like definitions of cyclic operads},
  author = {Jovana Obradović},
  journal= {arXiv preprint arXiv:1607.02438},
  year   = {2017}
}
R2 v1 2026-06-22T14:49:28.562Z