Galois theory and a new homotopy double groupoid of a map of spaces

The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes constructions by others of a 2-groupoid, cat^1-group or crossed module. An advantage of our construction is that the double groupoid can give an algebraic model of a foliated bundle.