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We investigate the properties of categories of G C -flat R-modules where C is a semidualizing module over a commutative noetherian ring R. We prove that the category of all G C -flat R-modules is part of a weak AB-context, in the terminology of Hashimoto. In particular, this allows us to deduce the existence of certain Auslander-Buchweitz approximations for R-modules of finite G C -flat dimension. We also prove that two procedures for building R-modules from complete resolutions by certain subcategories of G C -flat R-modules yield only the modules in the original subcategories.

AB-Contexts and Stability for Gorenstein Flat Modules with Respect to Semidualizing Modules