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 $YD(H)$ is not abelian?

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# Is the category of Yetter-Drinfeld modules abelian?

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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 $YD(H)$ is not abelian?

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