# Bialgebra

In the notes, we have that, given an algebra $(H,m,u)$ and coalgebra $(H,\Delta, \epsilon)$, we have a bialgebra if $\Delta, \epsilon$ are algebra maps. I assume an algebra homomorphism qualifies as an algebra map.

Is this method equivalent to checking the commutativity of the four diagrams given by Sweedler?

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### One comment

1. Brian,
– algebra map = algebra homomorphism
– Checking these conditions is indeed equivalent to checking Sweedler’s four diagrams (which just restate the conditions in diagram form)