We modify a previous result, which showed that certain diagrams of spaces are essentially simplicial monoids, to construct diagrams of spaces which model simplicial groups. Furthermore, we show that these diagrams can be generalized to models for Segal groupoids. We then modify Segal's model for simplicial abelian monoids in such a way that it becomes a model for simplicial abelian groups.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.149-174.