  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 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.
