We will give an overview of TQFTs with defects along the lines of the preprint 3-dimensional defect TQFTs and their tricategories by Carqueville, Meusburger and Schaumann. In this paper ordinary Atiyah type functorial TQFTs on 2+1 cobordisms are generalized to 2+1 stratified cobordisms with decorations in a certain graph structure. The decoration graph structure together with a given TQFT of this type then give rise to a linear Gray-category with duals. This provides a unifying framework for well known 2+1 TQFTs.

See arxiv.org/abs/1603.01171