A CATEGORICAL APPROACH TO ALGEBRAS an‎d COALGEBRAS

Algebraic and coalgebraic structures are often handled independently. In this survey we want to show that they both show up naturally when approaching them from a categorical point of view. Azumaya, Frobenius, separable, and Hopf algebras are obtained when both notions are combined. The starting point and guiding lines for this approach are given by adjoint pairs of functors and their elementary properties.