We use 3d defect TQFTs and state sum models with defects to give a gauge theoretical formulation of Kitaev's quantum double model (for a finite group) and the (untwisted) Dijkgraaf-Witten TQFT with defects. This leads to a simple description in terms of embedded quivers, groupoids and their representations. Defect Dijkgraaf-Witten TQFT is then formulated in terms of spans of groupoids and their representations.

This is work in progress with João Faria Martins (University of Leeds).