The main result of this page is that
Theorem
Every Frobenius algebra has a unique coalgebra structure for which the Frobenius form is the counit which is
-linear.
Conversely, given any coalgebra,
The Category of Frobenius Algebras
Frobenius Homomorphism
A Frobenius homomorphism between two Frobenius algebras is an algebra homomorphism that is also a coalgebra homomorphism.