Some remarks on equivariant algebraic geometry

It is common to view Hopf algebras as symmetries of noncommutative (nc) spaces, but in view of nc spaces as categories, and search for nonaffine symmetry objects this is not that sensible. I would like to give few remarks on the role of relative setup, actions of monoidal categories and distributive laws in setting up a more flexible approach to symmetries of nc spaces. These are rather trivial observations which are overlooked by most practitioners of the subject so it is an easy and a good task to present the few principles and examples.

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