Poincaré duality isomorphisms in tensor categories

If for a vector space V of dimension g over a characteristic zero field we denote by ∧iV its alternating powers, and by V∨ its linear dual, then there are natural Poincaré isomorphisms:∧iV∨≅∧g−iV. We describe an analogous result for objects in rigid pseudo-abelian Q-linear ACU tensor categories.