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

2019/10/02 by Di Liberti, Ivan · 1 citation
#Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)

paper · doi:10.48550/arxiv.1910.01014

Abstract

We study codensity monads T induced by (mostly small, mostly dense) full subcategories A ⊂ 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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• Demystifying Codensity Monads via Duality

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