Ultracategories via Kan extensions of relative monads
Category Theory
2025-06-12 v1
Abstract
Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, under suitable hypotheses, the left oplax Kan extension of a relative 2-monad on categories yields a pseudomonad having the same category of colax algebras. In particular, we apply this to the study of ultracategories to recover the 'ultracompletion' pseudomonad.
Cite
@article{arxiv.2506.09788,
title = {Ultracategories via Kan extensions of relative monads},
author = {Umberto Tarantino and Joshua Wrigley},
journal= {arXiv preprint arXiv:2506.09788},
year = {2025}
}