Codensity: Isbell duality, pro-objects, compactness and accessibility.

@article{Liberti2019CodensityID,
  title={Codensity: Isbell duality, pro-objects, compactness and accessibility.},
  author={Ivan Di Liberti},
  journal={arXiv: Category Theory},
  year={2019}
}
We study codensity monads $T$ induced by (mostly small, mostly dense) full subcategories $A \subset K$. 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. 
3 Citations
The Scott adjunction

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