  By introducing $N$-framed quivers, we define the localization of Lusztig's
sheaves for $N$-framed quivers and functors $E^{(n)}_{i}, F^{(n)}_{i},
K^{\pm}_i$ for localizations. This gives a categorical realization of tensor
products of integrable highest weight modules of the quantized enveloping
algebra. The simple perverse sheaves in the localization provide the canonical
basis of tensor products. It is bar-invariant and has positivity. Moreover, we
give a categorical interpretation of the Yang-Baxter equation.
