Bar categories and star operations (Q838964)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bar categories and star operations |
scientific article |
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Bar categories and star operations (English)
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1 September 2009
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The category of complex vector spaces admits an involutive endofunctor taking each vector space to itself with conjugate scalar multiplication. The bar categories defined here abstract this to a pseudo-involutive endofunctor on a monoidal category; there are some more isomorphisms and some axioms. Categories of modules (or comodules) over a star-Hopf algebra are clear examples; but there are others involving flip-star-, and quasi-star-Hopf algebras. A Tannaka-like result reconstructs a star-Hopf algebra from a (strong) bar category with appropriate fibre functor.
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monoidal category
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tensor category
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Hopf algebra
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Tannaka reconstruction
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conjugate scalar multiplication
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