Generalised bialgebras and entwined monads and comonads

• Muriel Livernet ^[1] ; Bachuki Mesablishvili ^[2] ; Robert Wisbauer ^[3]
  1. [1] Paris 13 University

     Paris 13 University

     Arrondissement de Saint-Denis, Francia

     
  2. [2] Tbilisi State University

     Tbilisi State University

     Georgia

     
  3. [3] Universidad Heinrich Heine de Düsseldorf, Germany

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• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 8 (August 2015), 2015, págs. 3263-3278
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.10.013
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• Resumen

  • J.-L. Loday has defined generalised bialgebras and proved structure theorems in this setting which can be seen as general forms of the Poincaré–Birkhoff–Witt and the Cartier–Milnor–Moore theorems. It was observed by the present authors that parts of the theory of generalised bialgebras are special cases of results on entwined monads and comonads and the corresponding mixed bimodules. In this article the Rigidity Theorem of J.-L. Loday is extended to this more general categorical framework.