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

21 Feb 2020  ·  Di Liberti Ivan ·

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. read more

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Category Theory General Topology Logic