Geodesic
Monoidal Kleisli bicategories and the arithmetic product of coloured symmetric sequences
Documenta mathematica, Tome 29 (2024) no. 3, pp. 627-702

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We extend the arithmetic product of species of structures and symmetric sequences studied by Maia and Méndez 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.
DOI : 10.4171/dm/950
Classification : 18N10, 18N15, 18M80, 18C20, 18M05
Mots-clés : Kleisli bicategory, double category, monoidal structure, symmetric sequence, species of structures 
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Nicola Gambino; Richard Garner; Christina Vasilakopoulou. Monoidal Kleisli bicategories and the arithmetic product of coloured symmetric sequences. Documenta mathematica, Tome 29 (2024) no. 3, pp. 627-702. doi: 10.4171/dm/950

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