Abstract
The aim of this paper is to form interactions among various full subcategories related to the category of static modules and the companion category. These full subcategories form cubical lattice diagrams over a pair of rings and possess many symmetrical properties. Natural equivalences among them via projective and injective Morita contexts are studied. Besides these, the above constructions have been used to extend stable Clifford theory over the tensor product of two bimodules which are the ingredients of a Morita context. Finally, some equivalences are derived by involving colocalization and localization over the trace ideals of an injective Morita context.