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arXiv · 2303.09873

Cloning systems and action operads

Javier Aramayona·Federico Cantero Morán·Víctor Carmona·Javier J. Gutiérrez
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Abstract

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

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Javier Aramayona, Federico Cantero Morán, Víctor Carmona, Javier J. Gutiérrez. 2023-03-17. Cloning systems and action operads. https://arxiv.org/abs/2303.09873

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