Monoidal Kleisli Bicategories and the Arithmetic Product of Coloured Symmetric Sequences
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866911771600617472 |
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| author | Gambino, Nicola Garner, Richard Vasilakopoulou, Christina |
| author_facet | Gambino, Nicola Garner, Richard Vasilakopoulou, Christina |
| contents | We extend the arithmetic product of species of structures and symmetric sequences studied by Maia and Mendez and by Dwyer and Hess to coloured symmetric sequences and show that it determines a normal oplax monoidal structure on the bicategory of coloured symmetric sequences. In order to do this, we establish general results on extending monoidal structures to Kleisli bicategories. Our approach uses monoidal double categories, which help us to attack the difficult problem of verifying the coherence conditions for a monoidal bicategory in an efficient way. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2206_06858 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Monoidal Kleisli Bicategories and the Arithmetic Product of Coloured Symmetric Sequences Gambino, Nicola Garner, Richard Vasilakopoulou, Christina Category Theory Algebraic Topology 18N10, 18N15, 18M80, 18C20, 18M05 We extend the arithmetic product of species of structures and symmetric sequences studied by Maia and Mendez and by Dwyer and Hess to coloured symmetric sequences and show that it determines a normal oplax monoidal structure on the bicategory of coloured symmetric sequences. In order to do this, we establish general results on extending monoidal structures to Kleisli bicategories. Our approach uses monoidal double categories, which help us to attack the difficult problem of verifying the coherence conditions for a monoidal bicategory in an efficient way. |
| title | Monoidal Kleisli Bicategories and the Arithmetic Product of Coloured Symmetric Sequences |
| topic | Category Theory Algebraic Topology 18N10, 18N15, 18M80, 18C20, 18M05 |
| url | https://arxiv.org/abs/2206.06858 |