Cloning systems and action operads

• Aramayona, Javier ; Cantero, Federico ; Carmona, Víctor ^[1] ; Javier José Gutiérrez Marín
  1. [1] Max Planck Institute for Mathematics in the Sciences

     Max Planck Institute for Mathematics in the Sciences

     Kreisfreie Stadt Leipzig, Alemania

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 70, Nº 1, 2026, págs. 79-113
• Idioma: inglés
• DOI: 10.5565/publmat7012604
• Texto completo no disponible (Saber más ...)
• Resumen

  • Action operads and cloning systems are, respectively, the main ingredients in Thumann’s and Witzel–Zaremsky’s approaches for axiomatically constructing Thompson-like groups. In this paper, we prove that action operads are equivalent to cloning systems that admit a certain extra structure, and which we call restricted operadic cloning systems. In addition, we describe their relationship with crossed interval groups and product categories.