Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures

By Marcelo P. Fiore, Nicola Gambino, Martin Hyland, Glynn Winskel. 2016

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e0082b22181cb8f429005f72331e5a615e6007c5