A CATEGORICAL APPROACH TO ALGEBRAS AND COALGEBRAS

Authors : Robert WİSBAUER

Pages : 153-173

Doi:10.24330/ieja.440239

View : 13 | Download : 12

Publication Date : 2018-07-05

Article Type : Research Paper

Abstract :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.
Keywords : Co, algebras co, monads, Frobenius algebras, separable algebras, Hopf algebras