Hopf algebra

Let $K$ be a commutative ring. A Hopf $K$ -algebra #m/def/ralg/hopf is a Hopf monoid in $K 𝖬 𝗈 𝖽$ . Thus it is a $K$ -bimonoid $H$ equipped with an antipous $𝜎 : H \to H$ , where in Sweedler notation the antipous law reads

\sum (𝑥) 𝜎 (𝑥 (1)) 𝑥 (2) = 𝜂 𝜖 = \sum (𝑥) 𝑥 (1) 𝜎 (𝑥 (2)) .

#state/develop | #lang/en | #SemBr