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Examples of categorification. (English) Zbl 0895.18004
The purpose of this paper is to consider several simple cases of the inverse relation to the Grothendieck rig construction as constructions of tensor and bitensor categories. The authors consider examples of categorifications and their relevance to the construction of TQFT’s. They restrict their attention to the case of an algebraically closed field $${\mathcal K}$$ because this covers the most interesting case of $${\mathcal K}={\mathbb{C}}$$ and removes the possibility of having objects in semi-simple categories whose endomorphism algebras are division-algebra extensions of the ground field. One of the examples of categorifications considered in this paper is the question of categorifying the simplest really non-trivial Hopf algebra: the Drinfel’d double of a finite (non-commutative) group algebra.
Reviewer: V.Abramov (Tartu)

##### MSC:
 18D05 Double categories, $$2$$-categories, bicategories and generalizations (MSC2010) 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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