We give an explicit description of the free path and loop groupoids in the Morita bicategory of translation topological groupoids.We prove that the free path groupoid of a discrete group acting properly on a topological space X is a translation groupoid given by the same group acting on the topological path space X I .We give a detailed description of based path and loop groupoids and show that both are equivalent to topological spaces.We also establish the notion of homotopy and fibration in this context.
