In this talk I will review the program of categorification of Verma modules of symmetrizable quantum Kac-Moody algebras and extend it to a categorification of tensor products of a Verma module and several integrable irreducibles. In the last part of the talk I will consider the case of $\mathfrak{sl}(2)$ and explain how its categorifications are endowed with an action of the Temperley-Lieb algebra of type B with two parameters. The material presented is based upon several collaborations with Grégoire Naisse, Ruslan Maksimau and Abel Lacabanne.