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, cat1 -group or crossed module. An advantage of our construction is that the double groupoid can give an algebraic model of a foliated bundle.1

• Type: Journal
• Year: 2004
• Where: ACS
• Authors: Ronald Brown, George Janelidze
• Keywords: ACS 2004, ACS 2007, Double, Groupoid, Kan Simplicial Sets