A recognition criterion for lax-idempotent pseudomonads
Category Theory
2025-12-22 v2
Abstract
We describe a simple criterion which makes it easy to recognise when a pseudomonad is lax-idempotent. The criterion concerns the behaviour of colax bilimits of arrows - certain comma objects - and is easy to verify in examples. Building on this, we obtain a new characterisation of lax-idempotent pseudomonads on 2-categories with colax bilimits of arrows.
Cite
@article{arxiv.2512.05631,
title = {A recognition criterion for lax-idempotent pseudomonads},
author = {John Bourke},
journal= {arXiv preprint arXiv:2512.05631},
year = {2025}
}
Comments
17 pages, slightly extended section on monadicity