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Huang, Lepowsky and Zhang have developed a module theory for vertex operatoralgebras that endows suitably chosen module categories with the structure ofbraided monoidal categories. Included in the theory is a functor which assignsto discretely strongly graded modules a contragredient module, obtained as agradewise dual. In this paper, we show that this gradewise dual endows themodule category with the structure of a ribbon Grothendieck-Verdier category.This duality structure is more general than that of a rigid monoidal category;in contrast to rigidity, it naturally accommodates the fact that a vertexoperator algebra and its gradewise dual need not be isomorphic as modules andthat the tensor product of modules over vertex operator algebras need not beexact.  We develop criteria which allow the detection of ribbon Grothendieck-Verdierequivalences and use them to explore ribbon Grothendieck-Verdier structures inthe example of the rank $n$ Heisenberg vertex operator algebra or chiral freeboson on a not necessarily full rank even lattice with arbitrary choice ofconformal vector. We show that these categories are equivalent, as ribbonGrothendieck-Verdier categories, to certain categories of graded vector spacesand categories of modules over a certain Hopf algebra.

Duality structures for module categories of vertex operator algebras and the Feigin Fuchs boson