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

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Authors

DI LIBERTI Ivan

Year of publication 2020
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1016/j.jpaa.2020.106379
Doi http://dx.doi.org/10.1016/j.jpaa.2020.106379
Keywords quantale; monads; bicategory
Description We study codensity monads T induced by (mostly small, mostly dense) full subcategories A subset of 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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