Skew monoidal structures on actegories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914102224355328 |
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| author | Procházková, Pavla |
| author_facet | Procházková, Pavla |
| contents | We present a construction of skew monoidal structures from strong actions. We prove that the existence of a certain adjoint allows one to equip the actegory with a skew monoidal structure and that this adjunction becomes monoidal. This construction provides a unifying framework for the description of several examples of skew monoidal categories. We also demonstrate how braidings on the original monoidal category of a given action induce braidings on the resulting skew monoidal structure on the actegory and describe sufficient conditions for closedness of the resulting skew monoidal structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Skew monoidal structures on actegories Procházková, Pavla Category Theory We present a construction of skew monoidal structures from strong actions. We prove that the existence of a certain adjoint allows one to equip the actegory with a skew monoidal structure and that this adjunction becomes monoidal. This construction provides a unifying framework for the description of several examples of skew monoidal categories. We also demonstrate how braidings on the original monoidal category of a given action induce braidings on the resulting skew monoidal structure on the actegory and describe sufficient conditions for closedness of the resulting skew monoidal structure. |
| title | Skew monoidal structures on actegories |
| topic | Category Theory |
| url | https://arxiv.org/abs/2506.06847 |