I felt like following up on Kate's question. There were some good motivational answers there. Given a pair of factors M < N, there is a standard way to construct a 2-category whose objects are M ...
So one way to categorify the natural numbers is to replace them with vector spaces. Then the dimension of the vector space reproduces the natural number. More generally you can categorify integers to ...
If (C,tensor,1) is a symmetric monoidal category and f:A-->B is a morphism of PROPs (or monoidal cats = colored PROPs), one gets a forgetful functor f^*:B-Alg(C)-->A-Alg(C) (where ...
The Reshetikhin-Turaev construction take as input a Modular Tensor Category (MTC) and spits out a 3D TQFT. I've been told that the other main construction of 3D TQFTs, the Turaev-Viro State sum ...
Any quantized universal enveloping algebra (in fact, any toplogically quasi-triangular Hopf algebra) has an (in its completion) an element u called the Drinfeld element which gives an isomorphism from ...
Is there a good monoidal structure on a category of integrable representations of a quantum affine algebra? In the ordinary affine Kac-Moody case, there is the usual tensor product (symmetric, adds ...
A pivotal monoidal category is called non-degenerate if the inner product (x,y) = Tr(xy*) (where y* is the dual map) is non-degenerate. As a rule of thumb non-degenerate is closely related to ...