The terminology topologizing subcategory is (probably) coming from the related notion of a topologizing filter from the localization theory of rings.

Properties

The classes of topologizing subcategories, reflective topologizing subcategories and coreflective topologizing subcategories are closed under Gabriel multiplication defined on the class of full subcategories of $A$. Given a (not necessarily unital) ring $R$, any reflective topologizing subcategory of $R$-$\mathrm{Mod}$ is coreflective.

A. L. Rosenberg, Noncommutative algebraic geometry and representations of quantized algebras, MIA 330, Kluwer Academic Publishers Group, Dordrecht, 1995. xii+315 pp. ISBN: 0-7923-3575-9

V. A. Lunts, A. L. Rosenberg, Differential calculus in noncommutative algebraic geometry I. D-calculus on noncommutative rings, MPI 1996-53 pdf

Last revised on November 19, 2011 at 15:18:52.
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