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Article

Lejay, Damien ; Le Grignou, Brice
Operads without coalgebras. (English). Higher Structures, vol. 4 (2020), issue 2, pp. 222-227
MSC: 18D50 | MR 4133169 | Zbl 1469.18026 | DOI: 10.21136/HS.2020.15
Keywords:
operads; coalgebras; cogebras
Summary:
We give an example of a non-trivial linear operad that only admits trivial coalgebras and give sufficient conditions ensuring that the cofree coalgebra functor be faithful.
References:
[1] Anel, Mathieu: Cofree coalgebras over operads and representative functions, September 2014. Arxiv1409.4688
[2] Joyal, André: Foncteurs analytiques et espèces de structures. In Gilbert Labelle and Pierre Leroux, editors, Combinatoire énumérative, pages 126–159, Berlin, Heidelberg. Springer Berlin Heidelberg
[3] May, J. Peter: Operads, algebras and modules. In James Stasheff Jean-Louis Loday and Alexander Voronov, editors, Operads: Proceedings of Renaissance Conferences, volume 202, pages 15–31. American Mathematical Society
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