In this paper we use Quillen's model structure given by Dwyer-Kan for the category of simplicial groupoids (with discrete object of objects) to describe in this category, in the simplicial language, the fundamental homotopy theoretical constructions of path and cylinder objects. We then characterize the associated left and right homotopy relations in terms of simplicial identities and give a simplicial description of the homotopy category of simplicial groupoids. Finally, we show loop and suspension functors in the pointed case.
Keywords: closed model category, path object, cylinder object, homotopy relation.
2000 MSC: 18G30, 55U35.
Theory and Applications of Categories, Vol. 7, 2000, No. 14, pp 263-283.