File:HopfAlgebra.png

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Commutative diagram for Hopf algebras.

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\begin{diagram}[vtrianglewidth=1.8em,tight]
& & H\otimes H & & \rTo^{\scriptstyle S\otimes \id} & & H\otimes H \\
& \ruTo^{\scriptstyle\Delta} & & & & & & \rdTo>{\scriptstyle\nabla} \\
H & & \rTo^{\scriptstyle \varepsilon} & & K & & \rTo^{\scriptstyle \eta} & & H \\
& \rdTo<{\scriptstyle\Delta} & & & & & & \ruTo>{\scriptstyle \nabla} \\
& & H\otimes H & & \rTo_{\scriptstyle \id\otimes S} & & H\otimes H \\
\end{diagram}