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Monoid-like definitions of cyclic operads

Authors
  • Obradovic, Jovana
Type
Preprint
Publication Date
Jul 08, 2016
Submission Date
Jul 08, 2016
Identifiers
arXiv ID: 1607.02438
Source
arXiv
License
Yellow
External links

Abstract

Guided by the microcosm principle of Baez and Dolan and by the algebraic definitions of operads given by Kelly and Fiore, we introduce two "monoid-like" definitions of cyclic operads, one for the "exchangable-output" characterisation and the other for the alternative "entries-only" characterisation, both within the framework of Joyal's theory of species of structures. Relying on a result of Lamarche coming from the descent theory 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.

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