N=2 supersymmetric Landau-Ginzburg models with a non-trivial IR fixed point provide an interesting laboratory to study superconformal field theories in two dimensions. Many interesting quantities can be determined algebraically, and we will look in particular at B-type interfaces which are described by matrix factorisations.

Their fusion is given by the tensor product of such factorisations which in general is difficult to compute. I present an idea how to describe the fusion of a certain class of interfaces in an efficient way. For this purpose we will study ‘fusion functors’ on the category of modules over the algebra of polynomials in the chiral superfields.