Partial H-modules form a biactegory over H-modules, and for pointed Hopf algebras with finitely many grouplikes the standard dilation functor is naturally isomorphic to the Hom-object {Apar, -}.
Abadie: Dilations of interaction groups that extend actions of Ore semigroups , J
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Globalization and the biactegory of partial modules
Partial H-modules form a biactegory over H-modules, and for pointed Hopf algebras with finitely many grouplikes the standard dilation functor is naturally isomorphic to the Hom-object {Apar, -}.