Duality in Tensor Categories
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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.
KeywordsHopf Algebra Tensor Category Quantum Dimension Object Versus Leave Adjoint
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