bialgebra (Q6196)

vector space which is both a unital associative algebra and a counital coassociative coalgebra in a compatible way

Language	Label	Description	Also known as
English	bialgebra	vector space which is both a unital associative algebra and a counital coassociative coalgebra in a compatible way

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{\begin{aligned}\Delta \circ \nabla &=\nabla \otimes \nabla \circ (\operatorname {id} \otimes \sigma \otimes \operatorname {id} )\circ \Delta \otimes \Delta \\\epsilon \otimes \epsilon &=\epsilon \circ \nabla \\\eta \otimes \eta &=\Delta \circ \eta \\\epsilon \circ \eta &=\operatorname {id} \end{aligned}}

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