A general framework will be discussed which unifies group equivariantisations and state sum models, in the context of topological quantum field theory (TQFT) in arbitrary dimension. After illustrating the construction and showcase some applications in dimension 2, I will outline general aspects of the construction and and discuss examples in 3 dimensions, including Turaev-Viro theory as an orbifold, as well as surface defects in quantised Chern-Simons theory. (Based on joint work with I. Runkel and G. Schaumann.)