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arXiv · 2104.10718

Actor of a crossed module of dialgebras via tetramultipliers

José Manuel Casas·Rafael Fernández-Casado·Xabier García-Martínez·Emzar Khmaladze
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Abstract

We study the representability of actions in the category of crossed modules of dialgebras via tetramultipliers. We deduce a pair of dialgebras in order to construct an object which, under certain circumstances, is the actor (also known as the split extension classifier). Moreover, we give give a full description of actions in terms of equations. Finally, we check that under the aforementioned circumstances, the center coincides with the kernel of the canonical map from a crossed module to its actor.

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José Manuel Casas, Rafael Fernández-Casado, Xabier García-Martínez, Emzar Khmaladze. 2021-04-21. Actor of a crossed module of dialgebras via tetramultipliers. https://arxiv.org/abs/2104.10718

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