Quantum Groups pp 339-367 | Cite as

Duality in Tensor Categories

Part of the Graduate Texts in Mathematics book series (GTM, volume 155)


In the previous chapter we defined braided tensor categories modelled on the category of braids. We now introduce a class of tensor categories mod-elled on framed tangles or ribbons. These are the so-called ribbon cate-gories. Their definition requires the concept of duality. However, when du-ality is involved, formulas quickly tend to become obscure and complex. To overcome this difficulty, we present a graphical calculus in which coloured tangle diagrams represent morphisms of tensor categories.


Hopf Algebra Tensor Category Quantum Dimension Object Versus Leave Adjoint 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur-C.N.R.S.StrasbourgFrance

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