Wide Morita contexts and equivalences of comodule categories
The authors introduce a purely categorical notion of Morita context (called ``wide Morita context'') between Abelian categories, which extends the classical notion of Morita context for module categories as well as Takeuchi's notion of Morita context for comodule categories [\textit{M. Takeuchi}, J. Fac. Sci., Univ. Tokyo, Sect. I A 24, No. 3, 629-644 (1977; Zbl 0385.18007)]. For this general notion of Morita context, they prove an extension of both Morita's theorem on categories of modules and of Takeuchi's theorem on comodule categories. As an application they obtain, for any Takeuchi Morita context, an equivalence between appropriate subcategories of the categories of comodules through certain modifications of the cotensor product functors (Theorem 4.2). This equivalence is similar to that obtained by Nicholson-Watters for module categories [\textit{W. K. Nicholson} and \textit{J. F. Watters}, Math. Proc. Camb. Philos. Soc. 103, No. 3, 399-408 (1988; Zbl 0673.16025)].
scientific article; zbMATH DE number 1308238