Wide Morita contexts and equivalences of comodule categories Original Research Article

We introduce a purely categorical notion of Morita context between abelian categories, which extends the classical notion of Morita context for module categories as well as the Takeuchiʹs notion of Morita context for comodule categories (Takeuchi, 1977). We prove an extension both of Moritaʹs theorem on categories of modules and of Takeuchiʹs theorem on comodule categories for our general notion of Morita context. As an application of our theory, we obtain an equivalence between certain comodule categories defined by any Takeuchiʹs Morita context similar to that obtained by Nicholson-Watters for module categories at (Nicholson and Watters, 1988).