Bialgebras and Hopf Algebras

Abstract

Let H be a $\mathbb {K}$-module. Recall that a bialgebra structure on H is defined by four morphisms

$$\begin{aligned} H\otimes H&\xrightarrow {m} H \xrightarrow {\varDelta } H\otimes H\;,\\ \mathbb {K}&\xrightarrow {\eta } H \xrightarrow {\varepsilon } \mathbb {K}\;, \end{aligned}$$

satisfying the following axioms, written as commutative diagrams.