engleski

Compatibility of (co)actions and localizations

Earlier, Lunts and Rosenberg studied a notion of compatibility of endofunctors with localization functors, with an application to the study of differential operators on noncommutative rings and schemes. Another compatibility -- of Ore localizations of an algebra with a comodule algebra structure over a given bialgebra -- introduced in my earlier work -- is here described also in categorical language, but the appropriate notion differs from that of Lunts and Rosenberg, and it involves a specific kind of distributive laws. Some basic facts about compatible localization follow from more general functoriality properties of associating comonads or even actions of monoidal categories to comodule algebras. We also introduce localization compatible pairs of entwining structures.

coaction; localization; distributive law; compatibility; noncommutative differential operators

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