2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131504We give a purely geometric categorification of tensor products of finite-dimensional simple $U_q(sl_2)$-modules and $R$-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification theorems are understood as consequences of Deligne's theory of weights.44pages, made up some mistakes in the proof of Theorem 4.2.4Representation TheoryQuantum Algebra17B37; 18F20; 14M15text