Compatibility of (co)actions and localizations

Details Compatibility of (co)actions and localizations Compatibility of (co)actions and localizations

2009-02-09

arxiv.org/abs/0902.1398v1

Mathematics

Quantum Algebra

preliminary version, posted earlier because of using and referencing some of present results in another works of mine

Scientific paper

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.

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