# 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.
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#### References

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