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Is the category of Yetter-Drinfeld modules abelian?
Is $YD(H)$ the category of Yetter--Drinfeld modules over a Hopf algebra (defined over a field $k$) necessarily abelian? If not then what is the simplest example of a Hopf algebra $H$ for which $YD(H)$ ...
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Abelian category from the category of Hopf algebras
The kernel of a Hopf algebra map $\phi:H_1 \to H_2$ is in general not a Hopf
sub-algebra of $H_1$. Is there some replacement or alteration of the notion
of a kernel in the Hopf algebra setting. Same ...