The knot categorification problem is to find the theory that categorifies quantum link invariants which works uniformly with respect to the choice of a Lie algebra, and originates from geometry and physics. The solution comes from a new relation between homological mirror symmetry and representation theory. The symplectic geometry side of mirror symmetry is a theory generalizing Heegard–Floer theory. The generalization corresponds to replacing gl(1|1) by an arbitrary Lie algebra. The theories can be solved exactly.