A CATEGORICAL APPROACH TO ALGEBRAS AND COALGEBRAS

Year 2018, Volume: 24 Issue: 24, 153 - 173, 05.07.2018

Robert Wisbauer

https://doi.org/10.24330/ieja.440239

Cited By: 1

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

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