Abstract:

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 $((\ )^*,(\ )^{o})$ is an adjoint pair
(cf.Theorem 3),  some nice properties of functor
( )$^{o}$ are obtained. Finally Theoram 4 provides that the cotensor product is
the dual of the tensor product by $(M \otimes _A N)^o \cong M^o
\Box _{A^o} N^o$. Moreover, the result Hom$_A (M,N) \cong {\rm Com} _{A^o}
 (N^o,M^o)$ is proved for finite related modules $M,N$ over a reflexive
algebra $A$.

Key words: Universal dual comodule, Hopf algebras, cotensor product, adjoint pair