Complementary projection defects and decomposition

A bstract As put forward in [1] topological quantum field theories can be projected using so-called projection defects. The theory and its correlation functions completely realized within the unprojected one. An interesting example is case of associated to IR fixed points renormalization group flows, which by this method inside UV. In note we show that defects triangulated defect categories (such as 2d topologically twisted $$ \mathcal{N} N = (2 , 2) theories) always come with complementary defects, decomposes into two We demonstrate context Landau-Ginzburg orbifold theories.