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

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.

20 pages. Final version. Accepted by Journal of Pure and Applied Algebra

References in corpus (2)

• Erratum and Addendum: The factorization of the Giry monad
• Characterizing Giry-algebras as coseparable super convex spaces

Cited by in corpus (3)

• Formal Model Theory & Higher Topology
• On Vector Spaces with Formal Infinite Sums
• Filtered bicolimit presentations of locally presentable linear categories, Grothendieck categories and their tensor products