  We characterize noncommutative Frobenius algebras A in terms of the existence
of a coproduct which is a map of left A^e-modules. We show that the category of
right (left) comodules over A, relative to this coproduct, is isomorphic to the
category of right (left) modules. This isomorphism enables a reformulation of
the cotensor product of Eilenberg and Moore as a functor of modules rather than
comodules.
  We prove that the cotensor product M \Box N of a right A-module M and a left
A-module N is isomorphic to the vector space of homomorphisms from a particular
left A^e-module D to N \otimes M, viewed as a left A^e-module. Some properties
of D are described. Finally, we show that when A is a symmetric algebra, the
cotensor product M \Box N and its derived functors are given by the Hochschild
cohomology over A of N \otimes M.
