Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures
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.
Cite
@article{arxiv.1612.03678,
title = {Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures},
author = {Marcelo Fiore and Nicola Gambino and Martin Hyland and Glynn Winskel},
journal= {arXiv preprint arXiv:1612.03678},
year = {2019}
}
Comments
v3: Following referee comments: some material reorganised, presentation streamlined, definition of lax idempotent relative pseudomonad rephrased in terms of extensions. 32 pages. Accepted for publication in Selecta Mathematica (New Series)