The Landau-Ginzburg/CFT correspondence as first proposed by D. Gepner in 1990 relates certain 2d RCFTs (Kazama-Suzuki models) to Landau-Ginzburg theories (via a choice of superpotential). While originally a correspondence of bulk theories, a similar correspondence of solutions to boundary conditions has been constructed for a number of explicit models, including the A-type minimal model aka the SU(2)/U(1) KS model. Here, for B-type boundary conditions, maximally symmetric ("rational") solutions for the RCFT boundary problem (Cardy branes) are associated  to certain elementary matrix factorizations in the LG theory. To find such a "dictionary" for more general setups is a very non-trivial problem, already for the SU(3)/U(2) KS models. While some partial "dictionary" can be obtained in a "pedestrian way" [NB,1005.2117], the full solution requires some more sophisticated methods. As I will present in this talk, one may construct a closed functor algebra which not only allows to obtain an explicit "dictionary" of Cardy branes to matrix factorizations, but which also induces a set of topological defects for the LG theory that precisely matches the structure of such defects for the RCFT. This provides in particular some to the best of our knowledge new, physically motivated structure on the triangulated category of matrix-(bi)-factorizations, and I will also comment on some possible generalizations.