Poincar\'e duality isomorphisms in tensor categories

If for a vector space V of dimension g over a characteristic zero field we denote by ${\wedge }^{i}V$ its alternating powers, and by $V^{\vee }$ its linear dual, then there are natural Poincar'e isomorphisms: $\wedge^i V^\vee \cong \wedge^{g-i} V$. We describe an analogous result for objects in rigid pseudo-abelian $\mathbb{Q}$-linear ACU tensor categories.