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 a basis of the tensor product. We prove that this basis coincides with the canonical basis of tensor product in the sense of Lusztig and Bao-Wang. Moreover, we give a categorical interpretation of the Yang-Baxter equation.
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