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Differential calculi on noncommutative bundles
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We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a connection with respect to a differential calculus and consider questions of existence and uniqueness. At the end these constructions are applied to basic examples of noncommutative bundles over a coquasitriangular Hopf algebra.
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On quantum $G$-structures
A quantum G-structure, defined as a reduction of a quantum frame resolution, itself forms a quantum frame resolution under a covariant first-order differential calculus.
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