A note on "Modules, Comodules, and Cotensor Products over Frobenius Algebras"

This is a note on Abrams' paper "Modules, Comodules, and Cotensor Products over Frobenius Algebras, Journal of Algebras" (1999). With the application of Frobenius coordinates developed recently by Kadison, one has a direct proof of Abrams' characterization for Frobenius algebras in terms of comultiplication (see L. Kadison (1999)). For any Frobenius algebra, by using the explicit comultiplication, the explicit correspondence between the category of modules and the category of comodules is obtained. Moreover, with this we give very simplified proofs and improve Abrams' results on the Hom functor description of cotensor functor.