Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures

Abstract

We introduce the notion of a relative pseudomonad, which generalizes the notion of a pseudomonad, and define the Kleisli bicategory associated to a relative pseudomonad. We then present an efficient method to define pseudomonads on the Kleisli bicategory of a relative pseudomonad. The results are applied to define several pseudomonads on the bicategory of profunctors in an homogeneous way and provide a uniform approach to the definition of bicategories that are of interest in operad theory, mathematical logic, and theoretical computer science.

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Correspondence to N. Gambino.

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Fiore, M., Gambino, N., Hyland, M. et al. Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures. Sel. Math. New Ser. 24, 2791–2830 (2018). https://doi.org/10.1007/s00029-017-0361-3

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  • 18C20
  • 18D50