framed bundles; affine bundles; quot scheme flat localizations of Abelian categories; structure presheaves of modules; quantized algebras; noncommutative schemes in categories; left spectrum; maximal left ideals; completely prime left ideals; categories of rings; Levitzki radical; quasi-affine schemes; projective spectra; quantized rings; quantum planes; algebra of \(q\)-differential operators; Weyl algebras; quantum envelopes; coordinate rings; generalized Weyl algebras; skew polynomial rings; Serre subcategories; Grothendieck categories; hyperbolic rings; skew PBW monads; monoidal category; Kac-Moody and Virasoro Lie algebras; semigroup-graded monads; Gabriel-Krull dimension 