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We show that every partial representation of a connected Hopf algebra is global. Some interesting classes of partial representations of smash product Hopf algebras are studied, and a description of the partial "Hopf" algebra if the first tensorand is connected is given. If H is cocommutative and has finitely many grouplikes, this allows to see H₀ₑ as the weak Hopf algebra coming from a Hopf category.
Ferrazza et al. (Fri,) studied this question.