A very easy question I can't seem to answer: For a universal rform on a coquasitriangular Hopf algebra why is $r(a \otimes 1) = r(1 \otimes a) = \epsilon(a)$?
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Like David said, the proof is almost identical to the earlier one for $R$matrices: $r(x\otimes 1) = r\circ (id\otimes\mu)(x\otimes 1\otimes 1) = (r_{13}\ast r_{12})(x\otimes 1\otimes1)= \sum r(x'\otimes 1)r(x''\otimes 1) = (r \ast r)(x\otimes 1).$ Since $r$ is invertible, $r(x\otimes 1)=\epsilon(x)$. 

