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arXiv · 1910.01014

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

Ivan Di Liberti
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Abstract

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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Ivan Di Liberti. 2019-10-02. Codensity: Isbell duality, pro-objects, compactness and accessibility. https://doi.org/10.1016/j.jpaa.2020.106379

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