  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.
