Holmstrom Simplicial group

Jardine-Goerss chapter V treats simplicial groups and groupoids. For example, the category of sSets with an action of a simplicial group $G$ admits a model structure, and cofibrant objects correspond to principal $G$-fibrations.

There is an equivalence of homotopy cats (probably a Quillen equivalence) between simplicial groups and reduced simplicial sets. Similarly for simplicial groupoids and simplicial sets. See Jardine-Goerss V.6. They also describe Milnor’s FK construction, a simplicial group being a fibrant model for $\Omega \Sigma K$.

http://mathoverflow.net/questions/95026/connective-spectra-versus-simplicial-abelian-groups-very-basic-question

nLab page on Simplicial group