Displaying similar documents to “Examples of categorification”

Squared Hopf algebras and reconstruction theorems

Volodymyr Lyubashenko (1997)

Banach Center Publications

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Given an abelian 𝑉-linear rigid monoidal category 𝑉, where 𝑉 is a perfect field, we define squared coalgebras as objects of cocompleted 𝑉 ⨂ 𝑉 (Deligne's tensor product of categories) equipped with the appropriate notion of comultiplication. Based on this, (squared) bialgebras and Hopf algebras are defined without use of braiding. If 𝑉 is the category of 𝑉-vector spaces, squared (co)algebras coincide with conventional ones. If 𝑉 is braided, a braided Hopf algebra can be obtained...

Balanced coalgebroids.

Mccrudden, Paddy (2000)

Theory and Applications of Categories [electronic only]

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Representations, duals and quantum doubles of monoidal categories

Majid, Shahn

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[For the entire collection see Zbl 0742.00067.]The Tanaka-Krein type equivalence between Hopf algebras and functored monoidal categories provides the heuristic strategy of this paper. The author introduces the notion of a double cross product of monoidal categories as a generalization of double cross product of Hopf algebras, and explains some of the motivation from physics (the representation theory for double quantum groups).The Hopf algebra constructions are formulated in terms of...