Closed categories, star-autonomy, and monoidal comonads

This paper determines what structure is needed for internal homs in a monoidal category C to be liftable to the category C^G of Eilenberg-Moore coalgebras for a monoidal comonad G on C. We apply this to lift star-autonomy with the view to recasting the definition of quantum groupoid.

💡 Research Summary

This paper investigates the conditions under which the internal‑hom structure of a monoidal category (\mathcal C) can be lifted to the Eilenberg–Moore category (\mathcal C^{G}) of coalgebras for a monoidal comonad (G) on (\mathcal C). The authors begin by recalling that a closed monoidal category possesses, for each pair of objects (X,Y), an internal hom (