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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.06520 |
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| _version_ | 1866917948124299264 |
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| author | Rodríguez, Ramón González Raposo, Ana Belén Rodríguez |
| author_facet | Rodríguez, Ramón González Raposo, Ana Belén Rodríguez |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Categorical equivalences for Hopf trusses and their modules Rodríguez, Ramón González Raposo, Ana Belén Rodríguez Rings and Algebras 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. |
| title | Categorical equivalences for Hopf trusses and their modules |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2312.06520 |