Weak Bialgebras and Monoidal Categories
نویسندگان
چکیده
منابع مشابه
Weak Hopf Monoids in Braided Monoidal Categories
We develop the theory of weak bimonoids in braided monoidal categories and show them to be quantum categories in a certain sense. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid R leads to a weak Hopf monoid R ⊗ R.
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Let (M,⊗,1) be an abelian monoidal category. In order to investigate the structure of Hopf algebras with Chevalley property (i.e. Hopf algebras having the coradical a Hopf subalgebra) we define the Hochschild cohomology of an algebra A in M. Then we characterize those algebras A which have dimension less than or equal to 1 with respect to Hochschild cohomology. We use these results to prove tha...
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We associate to a group-like monoidal groupoid C a principal bundle E satisfying most of the axioms defining a biextension. The obstruction to the existence of a genuine biextension structure on E is exhibited. When this obstruction vanishes, the biextension E is alternating, and a trivialization of E induces a trivialization of C. The analogous theory for monoidal n-categories is also examined...
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A monoidal category is a category equipped with extra data, describing how objects and morphisms can be combined ‘in parallel’. This chapter introduces the theory of monoidal categories, and shows how our example categories Hilb, Set and Rel can be given a monoidal structure. We also introduce a visual notation called the graphical calculus, which provides an intuitive and powerful way to work ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2011
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2011.616438