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arXiv · 1612.03678

Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures

Marcelo Fiore·Nicola Gambino·Martin Hyland·Glynn Winskel
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Abstract

We introduce the notion of a relative pseudomonad, which generalises the notion of a pseudomonad, and define the Kleisli bicategory associated to a relative pseudomonad. We then present an efficient method to define pseudomonas 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, thus providing 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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Marcelo Fiore, Nicola Gambino, Martin Hyland, Glynn Winskel. 2016-12-12. Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures. https://doi.org/10.1007/s00029-017-0361-3

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