Gabi-monads on skew-closed categories are exactly the data needed to lift internal homs to Eilenberg-Moore categories; a gabi-monad is Hopf iff its parametric mates are invertible.
Monads on higher monoidal categories
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Gabi-Monads
Gabi-monads on skew-closed categories are exactly the data needed to lift internal homs to Eilenberg-Moore categories; a gabi-monad is Hopf iff its parametric mates are invertible.