The Universal Dual Comodule of Module in Hopf Algebras

The purpose of this paper is to present some dual properties of dual comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since (( )*, ( )°) is an adjoint pair (cf.Theorem 3), some nice properties of functor ( )° are obtained. Finally Theoram 4 provides that the cotensor product is the dual of the tensor product by ( M ⊗ A N ) ° ≅ M ° □ A ° N ° . Moreover, the result Hom A ( M, N ) ≅ Com A° ( N° , M°) is proved for finite related modules M, N over a reflexive algebra A.