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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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