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)

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