Ultracategories as colax algebras for a pseudo-monad on CAT
Category Theory
2025-08-26 v3
Abstract
We show a result inspired by a conjecture by Shulman claiming that ultracategories as defined by Lurie are normal colax algebras for a certain pseudo-monad on the category of categories CAT. Such definition allows us to regard left and right ultrafunctors as defined by Lurie as instances of lax/colax algebras morphisms
Cite
@article{arxiv.2502.20597,
title = {Ultracategories as colax algebras for a pseudo-monad on CAT},
author = {Ali Hamad},
journal= {arXiv preprint arXiv:2502.20597},
year = {2025}
}
Comments
Version 3. Fixed typos, Fixed many instances where mathematical notation was inconsistent, clarified some proofs