Timeline for What structure on a monoidal category would make its 2-category of module categories monoidal and braided?
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| Nov 10, 2010 at 2:51 | comment | added | Kevin McGerty | One should maybe be a little careful here: Lusztig (and later Rouquier, and Khovanov-Lauda) categorifies $U^+$ and thus shows it has a canonical basis. When he goes on to study the full quantum group he does indeed shift to $\dot{\mathbf U}$ as you say, finding a canonical basis for it, but he does by studying the tensor product of a highest and lowest weight module, not an arbitrary tensor product of irreducibles (in finite type you don't notice this, but in general it's a real distinction, and the constructions he uses don't really distinguish finite type in any way). | |
| Dec 8, 2009 at 9:58 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |