internalization and categorical algebra
algebra object (associative, Lie, …)
symmetric monoidal (∞,1)-category of spectra
The notion of relative pseudomonad generalizes that of pseudomonad, to be relative to a 2-functor, analogous to the notion of relative monad in the one-dimensional setting. This enables the construction of Kleisli bicategories of pseudomonads on Prof (e.g. for defining generalized multicategories) by means of pseudo-distributive laws as if the presheaf category construction were a monad with Prof as its Kleisli bicategory, even though it is not for size reasons.
An example is the free cocompletion construction on a small category.
Marcelo Fiore, Nicola Gambino, Martin Hyland, Glynn Winskel, Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures, arxiv
Nathanael Arkor, Philip Saville?, Andrew Slattery, Bicategories of algebras for relative pseudomonads, arXiv:2501.12510
An early observation that the bicategory of profunctors should be a Kleisli category for a relative monad is Appendice I.1(b) of:
Last revised on January 23, 2025 at 09:26:21. See the history of this page for a list of all contributions to it.