  As put forward in [arXiv:1907.12339] topological quantum field theories can
be projected using so-called projection defects. The projected theory and its
correlation functions can be completely realized within the unprojected one. An
interesting example is the case of topological quantum field theories
associated to IR fixed points of renormalization group flows, which by this
method can be realized inside the theories associated to the UV. In this note
we show that projection defects in triangulated defect categories (such as
defects in 2d topologically twisted N=(2,2) theories) always come with
complementary projection defects, and that the unprojected theory decomposes
into the theories associated to the two projection defects. We demonstrate this
in the context of Landau-Ginzburg orbifold theories.
