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Eilenberg-Moore Bicategories for Opmonoidal Pseudomonads

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arxiv 2402.11703 v1 pith:OXMIZZQM submitted 2024-02-18 math.CT

Adrian Miranda This is my paper · ORCID
classification math.CT
keywords eilenberg-mooremonoidalpseudomonadsresultsstructuresachieveanalysebicategories
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We analyse compatibility between monads and monoidal structures in the two-dimensional setting. We describe sufficient conditions for monoidal structures to lift to the Eilenberg-Moore pseudoalgebras. We then extend these results to braids, syllapses and symmetries. To achieve these results we define the Gray-tensor product of pseudomonads, and examine its interaction with the Eilenberg-Moore construction.

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  1. Bicategories of algebras for relative pseudomonads

    math.CT 2025-01 accept novelty 7.0 of 10

    For each relative pseudomonad T, the paper builds a terminal bicategory of T-pseudoalgebras, embeds the Kleisli bicategory into it, and characterizes pseudoalgebras for free cocompletion pseudomonads as cocomplete categories.

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