Poincaré duality isomorphisms in tensor categories

Abstract

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 Poincaré 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.

38 pages, submitted