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arXiv · 2312.06520

Categorical equivalences for Hopf trusses and their modules

Ramón González Rodríguez·Ana Belén Rodríguez Raposo
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Abstract

In this paper we introduce the notion of generalized invertible 1-cocycle in a strict braided monoidal category C, and we prove that the category of Hopf trusses is equivalent to the category of generalized invertible 1-cocycles. On the other hand, we also introduce the notions of module for a Hopf truss and for a generalized invertible 1-cocycle. We prove some functorial results involving these categories of modules and we show that the category of modules associated to a generalized invertible 1-cocycle is equivalent to a category of modules associated to a suitable Hopf truss. Finally, assuming that in C we have equalizers, we introduce the notion of Hopf-module in the Hopf truss setting and we obtain the Fundamental Theorem of Hopf modules associated to a Hopf truss.

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Ramón González Rodríguez, Ana Belén Rodríguez Raposo. 2025-03-07. Categorical equivalences for Hopf trusses and their modules. https://arxiv.org/abs/2312.06520

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