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Poincaré duality isomorphisms in tensor categories. (English) Zbl 1410.18011
Summary: If for a vector space $$V$$ of dimension $$g$$ over a characteristic zero field we denote by $$\bigwedge^i V$$ its alternating powers, and by $$V^\vee$$ its linear dual, then there are natural Poincaré isomorphisms: $\bigwedge^i V^\vee \cong \bigwedge^{g - i} V .$ We describe an analogous result for objects in rigid pseudo-abelian $$\mathbb{Q}$$-linear ACU tensor categories.
##### MSC:
 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 14C15 (Equivariant) Chow groups and rings; motives
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