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

Warning

This publication doesn't include Institute of Computer Science. It includes Faculty of Science. Official publication website can be found on muni.cz.

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	https://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.
Related projects:	Injektivita a monády v algebře a topologii