In this talk I will sketch the construction of the global DT sheaf, which provides a categorification of DT invariants. If supplied with a specific orientation, this construction can be carried out on the classical truncation of any -1 shifted symplectic derived scheme or derived Artin stack. This is done by using the orientation data to glue together sheaves of vanishing cycles on critical charts. Afterwards I will describe how this theory can be applied to the stack of local systems on a 3-manifold. In particular, I will discuss the example of lens spaces.