Codensity: Isbell duality, pro-objects, compactness and accessibility
Category Theory
2025-08-05 v3 General Topology
Logic
Abstract
We study codensity monads induced by (mostly small, mostly dense) full subcategories . These monads behave quite similarly, we show some connections with the Isbell duality, pro-finite objects and compact spaces. We prove that they are quite unlikely to be accessible. Finally, we introduce the notion of generically idempotent monad and comment its properties.
Cite
@article{arxiv.1910.01014,
title = {Codensity: Isbell duality, pro-objects, compactness and accessibility},
author = {Ivan Di Liberti},
journal= {arXiv preprint arXiv:1910.01014},
year = {2025}
}
Comments
20 pages. Final version. Accepted by Journal of Pure and Applied Algebra